Use for Questions 1-7:

Hector will roll two fair, six-sided dice at the same time. LetA = the event that at least one die lands with the number 3 facingup. Let B = the event that the sum of the two dice is less than5.

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

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

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

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

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

6. Calculate the probability that the sum of the two dice is notless than 5 if at least one die lands with 3 facing up. 7. Are Aand B independent? Explain your reasoning.

Use for question 10: A particular type of scan is used to try todetermine whether brain tumors are cancerous or not. Each time atumor 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% ofscans are “negative”. Among tumors that are NOT cancerous, 60% ofscans are “negative”, 37% of scans are “inconclusive” and 3% ofscans are “positive”. Historically, among all brain tumors, 67% arenot cancerous.

10. If a tumor is scanned and the result is labeled as“inconclusive” what is the probability that the tumor is notcancerous?