content-update

src/content-sources/oatutor/content-pool/a0d19dcInd1/a0d19dcInd1.json

@@ -0,0 +1,10 @@
+{
+    "id": "a0d19dcInd1",
+    "title": "Sampling With or Without Replacement",
+    "body": "Determine whether or not the following situation samples with or without replacement.",
+    "variabilization": {},
+    "oer": "https://openstax.org/details/books/introductory-statistics <OpenStax: Introductory Statistics>",
+    "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>",
+    "lesson": "3.2 Independent and Mutually Exclusive Events",
+    "courseName": "OpenStax: Introductory Stats"
+}

src/content-sources/oatutor/content-pool/a0d19dcInd1/steps/a0d19dcInd1a/a0d19dcInd1a.json

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+{
+    "id": "a0d19dcInd1a",
+    "stepAnswer": [
+        "With Replacement"
+    ],
+    "problemType": "MultipleChoice",
+    "stepTitle": "You have a fair, well-shuffled deck of $$52$$ cards. It consists of four suits. The suits are clubs, diamonds, hearts and spades. There are $$13$$ cards in each suit consisting of $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, $$9$$, $$10$$, J (jack), Q (queen), K (king) of that suit. Suppose you select three cards, The first card you pick out of the $$52$$ cards is the Q of spades. You put this card back, reshuffle the cards and pick a second card from the 52-card deck. It is the ten of clubs. You put this card back, reshuffle the cards and pick a third card from the 52-card deck. This time, the card is the Q of spades again. Your picks are {Q of spades, ten of clubs, Q of spades}.",
+    "stepBody": "",
+    "answerType": "string",
+    "variabilization": {},
+    "choices": [
+        "With Replacement",
+        "Without Replacement"
+    ]
+}

src/content-sources/oatutor/content-pool/a0d19dcInd1/steps/a0d19dcInd1a/tutoring/a0d19dcInd1aDefaultPathway.json

@@ -0,0 +1,24 @@
+[
+    {
+        "id": "a0d19dcInd1a-h1",
+        "type": "hint",
+        "dependencies": [],
+        "title": "Definition of With Replacement",
+        "text": "If each member of a population is replaced after it is picked, then that member has the possibility of being chosen more than once. When sampling is done with replacement, then events are considered to be independent, meaning the result of the first pick will not change the probabilities for the second pick.",
+        "variabilization": {},
+        "oer": "https://OATutor.io <OATutor>",
+        "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>"
+    },
+    {
+        "id": "a0d19dcInd1a-h2",
+        "type": "hint",
+        "dependencies": [
+            "a0d19dcInd1a-h1"
+        ],
+        "title": "Definition of Without Replacement",
+        "text": "When sampling is done without replacement, each member of a population may be chosen only once. In this case, the probabilities for the second pick are affected by the result of the first pick. The events are considered to be dependent or not independent.",
+        "variabilization": {},
+        "oer": "https://OATutor.io <OATutor>",
+        "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>"
+    }
+]

src/content-sources/oatutor/content-pool/a0d19dcInd17/a0d19dcInd17.json

@@ -0,0 +1,10 @@
+{
+    "id": "a0d19dcInd17",
+    "title": "Independent or Not?",
+    "body": "Determine if events A and B are independent:",
+    "variabilization": {},
+    "oer": "https://openstax.org/details/books/introductory-statistics <OpenStax: Introductory Statistics>",
+    "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>",
+    "lesson": "3.2 Independent and Mutually Exclusive Events",
+    "courseName": "OpenStax: Introductory Stats"
+}

src/content-sources/oatutor/content-pool/a0d19dcInd17/steps/a0d19dcInd17a/a0d19dcInd17a.json

@@ -0,0 +1,15 @@
+{
+    "id": "a0d19dcInd17a",
+    "stepAnswer": [
+        "Yes"
+    ],
+    "problemType": "MultipleChoice",
+    "stepTitle": "Let event A $$=$$ learning Spanish. Let event B $$=$$ learning German. Then A AND B $$=$$ learning Spanish and German. Suppose P(A) $$=$$ $$0.4$$ and P(B) $$=$$ $$0.2$$. P(A AND B) $$=$$ $$0.08$$. Are events A and B independent?",
+    "stepBody": "",
+    "answerType": "string",
+    "variabilization": {},
+    "choices": [
+        "Yes",
+        "No"
+    ]
+}

src/content-sources/oatutor/content-pool/a0d19dcInd17/steps/a0d19dcInd17a/tutoring/a0d19dcInd17aDefaultPathway.json

@@ -0,0 +1,12 @@
+[
+    {
+        "id": "a0d19dcInd17a-h1",
+        "type": "hint",
+        "dependencies": [],
+        "title": "Independent Definition",
+        "text": "We can determine whether or not two events are independent by seeing if P(A AND B) $$=$$ P(A)P(B).",
+        "variabilization": {},
+        "oer": "https://OATutor.io <OATutor>",
+        "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>"
+    }
+]

src/content-sources/oatutor/content-pool/a0d19dcInd18/a0d19dcInd18.json

@@ -0,0 +1,10 @@
+{
+    "id": "a0d19dcInd18",
+    "title": "Independent or Not?",
+    "body": "Determine if events A and B are independent:",
+    "variabilization": {},
+    "oer": "https://openstax.org/details/books/introductory-statistics <OpenStax: Introductory Statistics>",
+    "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>",
+    "lesson": "3.2 Independent and Mutually Exclusive Events",
+    "courseName": "OpenStax: Introductory Stats"
+}

src/content-sources/oatutor/content-pool/a0d19dcInd18/steps/a0d19dcInd18a/a0d19dcInd18a.json

@@ -0,0 +1,15 @@
+{
+    "id": "a0d19dcInd18a",
+    "stepAnswer": [
+        "No"
+    ],
+    "problemType": "MultipleChoice",
+    "stepTitle": "Let event A $$=$$ learning Spanish. Let event B $$=$$ learning German. Then A AND B $$=$$ learning Spanish and German. Suppose P(A) $$=$$ $$0.5$$ and P(B) $$=$$ $$0.5$$. P(A AND B) $$=$$ $$0.20$$. Are events A and B independent?",
+    "stepBody": "",
+    "answerType": "string",
+    "variabilization": {},
+    "choices": [
+        "Yes",
+        "No"
+    ]
+}

src/content-sources/oatutor/content-pool/a0d19dcInd18/steps/a0d19dcInd18a/tutoring/a0d19dcInd18aDefaultPathway.json

@@ -0,0 +1,12 @@
+[
+    {
+        "id": "a0d19dcInd18a-h1",
+        "type": "hint",
+        "dependencies": [],
+        "title": "Independent Definition",
+        "text": "We can determine whether or not two events are independent by seeing if P(A AND B) $$=$$ P(A)P(B).",
+        "variabilization": {},
+        "oer": "https://OATutor.io <OATutor>",
+        "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>"
+    }
+]

src/content-sources/oatutor/content-pool/a0d19dcInd19/a0d19dcInd19.json

@@ -0,0 +1,10 @@
+{
+    "id": "a0d19dcInd19",
+    "title": "Independent or Not?",
+    "body": "Determine if events A and B are independent:",
+    "variabilization": {},
+    "oer": "https://openstax.org/details/books/introductory-statistics <OpenStax: Introductory Statistics>",
+    "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>",
+    "lesson": "3.2 Independent and Mutually Exclusive Events",
+    "courseName": "OpenStax: Introductory Stats"
+}

src/content-sources/oatutor/content-pool/a0d19dcInd19/steps/a0d19dcInd19a/a0d19dcInd19a.json

@@ -0,0 +1,15 @@
+{
+    "id": "a0d19dcInd19a",
+    "stepAnswer": [
+        "Yes"
+    ],
+    "problemType": "MultipleChoice",
+    "stepTitle": "Let event A $$=$$ Playing Football. Let event B $$=$$ Playing American Football. Then A AND B $$=$$ Playing Football and American Football. Suppose P(A) $$=$$ $$0.1$$ and P(B) $$=$$ $$0.2$$. P(A AND B) $$=$$ $$0.02$$. Are events A and B independent?",
+    "stepBody": "",
+    "answerType": "string",
+    "variabilization": {},
+    "choices": [
+        "Yes",
+        "No"
+    ]
+}

src/content-sources/oatutor/content-pool/a0d19dcInd19/steps/a0d19dcInd19a/tutoring/a0d19dcInd19aDefaultPathway.json

@@ -0,0 +1,12 @@
+[
+    {
+        "id": "a0d19dcInd19a-h1",
+        "type": "hint",
+        "dependencies": [],
+        "title": "Independent Definition",
+        "text": "We can determine whether or not two events are independent by seeing if P(A AND B) $$=$$ P(A)P(B).",
+        "variabilization": {},
+        "oer": "https://OATutor.io <OATutor>",
+        "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>"
+    }
+]

src/content-sources/oatutor/content-pool/a0d19dcInd2/a0d19dcInd2.json

@@ -0,0 +1,10 @@
+{
+    "id": "a0d19dcInd2",
+    "title": "Sampling With or Without Replacement",
+    "body": "Determine whether or not the following situation samples with or without replacement.",
+    "variabilization": {},
+    "oer": "https://openstax.org/details/books/introductory-statistics <OpenStax: Introductory Statistics>",
+    "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>",
+    "lesson": "3.2 Independent and Mutually Exclusive Events",
+    "courseName": "OpenStax: Introductory Stats"
+}

src/content-sources/oatutor/content-pool/a0d19dcInd2/steps/a0d19dcInd2a/a0d19dcInd2a.json

@@ -0,0 +1,15 @@
+{
+    "id": "a0d19dcInd2a",
+    "stepAnswer": [
+        "With Replacement"
+    ],
+    "problemType": "MultipleChoice",
+    "stepTitle": "You have a fair, well-shuffled deck of $$52$$ cards. It consists of four suits. The suits are clubs, diamonds, hearts and spades. There are $$13$$ cards in each suit consisting of $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, $$9$$, $$10$$, J (jack), Q (queen), K (king) of that suit. Three cards are picked at random. Suppose you know that the picked cards are Q of spades, K of hearts and Q of spades. Can you decide if the sampling was with or without replacement?",
+    "stepBody": "",
+    "answerType": "string",
+    "variabilization": {},
+    "choices": [
+        "With Replacement",
+        "Without Replacement"
+    ]
+}

src/content-sources/oatutor/content-pool/a0d19dcInd2/steps/a0d19dcInd2a/tutoring/a0d19dcInd2aDefaultPathway.json

@@ -0,0 +1,24 @@
+[
+    {
+        "id": "a0d19dcInd2a-h1",
+        "type": "hint",
+        "dependencies": [],
+        "title": "Definition of With Replacement",
+        "text": "If each member of a population is replaced after it is picked, then that member has the possibility of being chosen more than once. When sampling is done with replacement, then events are considered to be independent, meaning the result of the first pick will not change the probabilities for the second pick.",
+        "variabilization": {},
+        "oer": "https://OATutor.io <OATutor>",
+        "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>"
+    },
+    {
+        "id": "a0d19dcInd2a-h2",
+        "type": "hint",
+        "dependencies": [
+            "a0d19dcInd2a-h1"
+        ],
+        "title": "Definition of Without Replacement",
+        "text": "When sampling is done without replacement, each member of a population may be chosen only once. In this case, the probabilities for the second pick are affected by the result of the first pick. The events are considered to be dependent or not independent.",
+        "variabilization": {},
+        "oer": "https://OATutor.io <OATutor>",
+        "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>"
+    }
+]

src/content-sources/oatutor/content-pool/a0d19dcInd20/a0d19dcInd20.json

@@ -0,0 +1,10 @@
+{
+    "id": "a0d19dcInd20",
+    "title": "Independent or Not?",
+    "body": "Determine if events A and B are independent:",
+    "variabilization": {},
+    "oer": "https://openstax.org/details/books/introductory-statistics <OpenStax: Introductory Statistics>",
+    "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>",
+    "lesson": "3.2 Independent and Mutually Exclusive Events",
+    "courseName": "OpenStax: Introductory Stats"
+}

src/content-sources/oatutor/content-pool/a0d19dcInd20/steps/a0d19dcInd20a/a0d19dcInd20a.json

@@ -0,0 +1,15 @@
+{
+    "id": "a0d19dcInd20a",
+    "stepAnswer": [
+        "No"
+    ],
+    "problemType": "MultipleChoice",
+    "stepTitle": "Let event A $$=$$ eating Lunch. Let event B $$=$$ eating Dinner. Then A AND B $$=$$ learning Spanish and German. Suppose P(A) $$=$$ $$0.5$$ and P(B) $$=$$ $$0.5$$. P(A AND B) $$=$$ $$0.1$$. Are events A and B independent?",
+    "stepBody": "",
+    "answerType": "string",
+    "variabilization": {},
+    "choices": [
+        "Yes",
+        "No"
+    ]
+}

src/content-sources/oatutor/content-pool/a0d19dcInd20/steps/a0d19dcInd20a/tutoring/a0d19dcInd20aDefaultPathway.json

@@ -0,0 +1,12 @@
+[
+    {
+        "id": "a0d19dcInd20a-h1",
+        "type": "hint",
+        "dependencies": [],
+        "title": "Independent Definition",
+        "text": "We can determine whether or not two events are independent by seeing if P(A AND B) $$=$$ P(A)P(B).",
+        "variabilization": {},
+        "oer": "https://OATutor.io <OATutor>",
+        "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>"
+    }
+]

src/content-sources/oatutor/content-pool/a0d19dcInd21/a0d19dcInd21.json

@@ -0,0 +1,10 @@
+{
+    "id": "a0d19dcInd21",
+    "title": "Mutually Exclusive or Not?",
+    "body": "Determine if events A and B are mutually exclusive:",
+    "variabilization": {},
+    "oer": "https://openstax.org/details/books/introductory-statistics <OpenStax: Introductory Statistics>",
+    "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>",
+    "lesson": "3.2 Independent and Mutually Exclusive Events",
+    "courseName": "OpenStax: Introductory Stats"
+}

src/content-sources/oatutor/content-pool/a0d19dcInd21/steps/a0d19dcInd21a/a0d19dcInd21a.json

@@ -0,0 +1,15 @@
+{
+    "id": "a0d19dcInd21a",
+    "stepAnswer": [
+        "Yes"
+    ],
+    "problemType": "MultipleChoice",
+    "stepTitle": "Let event A $$=$$ eating Lunch. Let event B $$=$$ eating Dinner. Then A AND B $$=$$ learning Spanish and German. Suppose P(A) $$=$$ $$0.5$$ and P(B) $$=$$ $$0.5$$. P(A AND B) $$=$$ $$0$$. Are events A and B mutually exclusive?",
+    "stepBody": "",
+    "answerType": "string",
+    "variabilization": {},
+    "choices": [
+        "Yes",
+        "No"
+    ]
+}

src/content-sources/oatutor/content-pool/a0d19dcInd21/steps/a0d19dcInd21a/tutoring/a0d19dcInd21aDefaultPathway.json

@@ -0,0 +1,12 @@
+[
+    {
+        "id": "a0d19dcInd21a-h1",
+        "type": "hint",
+        "dependencies": [],
+        "title": "Mutually Exclusive Definition",
+        "text": "A and B are mutually exclusive if P(A and B) $$=$$ $$0$$.",
+        "variabilization": {},
+        "oer": "https://OATutor.io <OATutor>",
+        "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>"
+    }
+]

src/content-sources/oatutor/content-pool/a0d19dcInd22/a0d19dcInd22.json

@@ -0,0 +1,10 @@
+{
+    "id": "a0d19dcInd22",
+    "title": "Mutually Exclusive or Not?",
+    "body": "Determine if events A and B are mutually exclusive:",
+    "variabilization": {},
+    "oer": "https://openstax.org/details/books/introductory-statistics <OpenStax: Introductory Statistics>",
+    "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>",
+    "lesson": "3.2 Independent and Mutually Exclusive Events",
+    "courseName": "OpenStax: Introductory Stats"
+}

src/content-sources/oatutor/content-pool/a0d19dcInd22/steps/a0d19dcInd22a/a0d19dcInd22a.json

@@ -0,0 +1,15 @@
+{
+    "id": "a0d19dcInd22a",
+    "stepAnswer": [
+        "No"
+    ],
+    "problemType": "MultipleChoice",
+    "stepTitle": "Let event A $$=$$ eating Lunch. Let event B $$=$$ eating Dinner. Then A AND B $$=$$ learning Spanish and German. Suppose P(A) $$=$$ $$0.5$$ and P(B) $$=$$ $$0.5$$. P(A AND B) $$=$$ $$0.1$$. Are events A and B mutually exclusive?",
+    "stepBody": "",
+    "answerType": "string",
+    "variabilization": {},
+    "choices": [
+        "Yes",
+        "No"
+    ]
+}

src/content-sources/oatutor/content-pool/a0d19dcInd22/steps/a0d19dcInd22a/tutoring/a0d19dcInd22aDefaultPathway.json

@@ -0,0 +1,12 @@
+[
+    {
+        "id": "a0d19dcInd22a-h1",
+        "type": "hint",
+        "dependencies": [],
+        "title": "Mutually Exclusive Definition",
+        "text": "A and B are mutually exclusive if P(A and B) $$=$$ $$0$$.",
+        "variabilization": {},
+        "oer": "https://OATutor.io <OATutor>",
+        "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>"
+    }
+]

src/content-sources/oatutor/content-pool/a0d19dcInd23/a0d19dcInd23.json

@@ -0,0 +1,10 @@
+{
+    "id": "a0d19dcInd23",
+    "title": "Independent or Not?",
+    "body": "Determine if events A and B are independent:",
+    "variabilization": {},
+    "oer": "https://openstax.org/details/books/introductory-statistics <OpenStax: Introductory Statistics>",
+    "license": "https://creativecommons.org/licenses/by/4.0/ <CC BY 4.0>",
+    "lesson": "3.2 Independent and Mutually Exclusive Events",
+    "courseName": "OpenStax: Introductory Stats"
+}

src/content-sources/oatutor/content-pool/a0d19dcInd23/steps/a0d19dcInd23a/a0d19dcInd23a.json

@@ -0,0 +1,15 @@
+{
+    "id": "a0d19dcInd23a",
+    "stepAnswer": [
+        "No"
+    ],
+    "problemType": "MultipleChoice",
+    "stepTitle": "In a particular college class, 60% of the students are female. Fifty percent of all students in the class have long hair. Forty-five percent of the students are female and have long hair. Of the female students, 75% have long hair. Let F be the event that a student is female. Let L be the event that a student has long hair. One student is picked randomly. Are the events of being female and having long hair independent?",
+    "stepBody": "",
+    "answerType": "string",
+    "variabilization": {},
+    "choices": [
+        "Yes",
+        "No"
+    ]
+}