Question

Use for Questions 1-7:

Hector will roll two fair, six-sided dice at the same time. Let A = the event that at least one die lands with the number 3 facing up. Let B = the event that the sum of the two dice is less than 5.

1. What is the correct set notation for the event that “at least one die lands with 3 facing up and the sum of the two dice is less than 5”?

2. Calculate the probability that at least one die lands with 3 facing up and the sum of the two dice is less than 5.

3. What is the correct set notation for the event that “at least one die lands with 3 facing up if the sum of the two dice is less than 5”?

4. Calculate the probability that at least one die lands with 3 facing up if the sum of the two dice is less than 5.

5. What is the correct set notation for the event that “the sum of the two dice is not less than 5 if at least one die lands with 3 facing up”?

6. Calculate the probability that the sum of the two dice is not less than 5 if at least one die lands with 3 facing up. 7. Are A and B independent? Explain your reasoning.

Use for question 10: A particular type of scan is used to try to determine whether brain tumors are cancerous or not. Each time a tumor is scanned, the result is reported as either “positive”, “negative” or “inconclusive”. Among tumors that are cancerous, 68% of scans are “positive”, 28% of scans are “inconclusive”, and 4% of scans are “negative”. Among tumors that are NOT cancerous, 60% of scans are “negative”, 37% of scans are “inconclusive” and 3% of scans are “positive”. Historically, among all brain tumors, 67% are not cancerous.

10. If a tumor is scanned and the result is labeled as “inconclusive” what is the probability that the tumor is not cancerous?

Answer 1

Hello Sir/ Mam

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Let A be the event that at least one die lands with the number 3 facing up.

Let B be the event that the sum of the two dice is less than 5.

Then, P(A) = 11/36 and P(B) = 6/36 and P(A B) = 15/36

1.  The correct set notation for the event that “at least one die lands with 3 facing up and the sum of the two dice is less than 5” is

2.

3. The correct set notation for the event that “at least one die lands with 3 facing up if the sum of the two dice is less than 5” is

4.

5. The correct set notation for the event that “the sum of the two dice is not less than 5 if at least one die lands with 3 facing up” is

6.

7. No, A and B are not inependent as .

I hope this solves your doubt.

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