8. The event A and B are mutually exclusive. IfP (A)-0.30, and P (8)-0.20. What

Question

8. The event A and B are mutually exclusive. IfP (A)-0.30, and P (8)-0.20. What is the probability of either A or B occurring? What is the probability that neither A nor B will happen? 9. Supposing P (A)-0.75 and P (BA) 0.40. What is the probability of A and B? 10. A survey of the stores in the Brons revealed 40 percent had pharmacy, 50 percent has a floral shop, and 70 percent had a deli. Supposed 10 percent of the stores have all three departments, 30 percent had both pharmacy and a deli, 25 percent have both a floral shop and a deli, and 20 percent have both a pharmacy and floral shop. (a) What is the probability of selecting a store at random and finding it has both a pharmacy and a floral shop? (b) What is the probability of selecting a store at random and finding it has both a pharmacy and a deli? c) What is the probability of selecting a store that does not have all three departments?

Explanation / Answer

8) For mutually exclusive events, P(A or B) = P(A) + P(B)

= 0.3 + 0.2

= 0.5

9) P(B | A) = P(A & B) / P(A)

P(A & B) = P(A) x P(B|A)

= 0.75x0.4

= 0.3

10) a) P(both pharmacy and floral shop) = 20%

= 0.20

b) P(pharmacy and deli) = 0.30

c) P(does not have all three departments) = 1 - P(Having all three departments)

= 1 - 0.10

= 0.90

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