Question

Let A and B be mutually exclusive events with P(A)=0.28 and P(B)=0.38. a. Calculate P(A∩B). (Round your answer to 2 decimal places.) P(A∩B) b. Calculate P(A∪B). (Round your answer to 2 decimal places.) P(A∪B) c. Calculate P(A∣B). (Round your answer to 2 decimal places.) Let A and B be independent events with P(A)=0.42 and P(B)=0.52. a. Calculate P(A∩B). (Round your answer to 2 decimal places.) P(A∩B) b. Calculate P((A∪​∪​)C). (Round your answer to 2 decimal places.) P((A∪B)c) c. Calculate P(A∣B). (Round your answer to 2 decimal places.)

Answer 1

For mutually exclusive events, the probability of both events occurring simultaneously is 0, and the probability of one of the events occurring given the other event has occurred is also 0. For independent events, the probability of both events occurring is the product of their individual probabilities.

Step-by-step explanation:

For the first scenario where A and B are mutually exclusive events with P(A)=0.28 and P(B)=0.38:

• a. Calculate P(A∩B). Since A and B are mutually exclusive, P(A∩B) = 0. Therefore, the probability of both A and B occurring is 0.00.
• b. Calculate P(A∪B). The probability of either A or B occurring is P(A) + P(B), which is 0.28 + 0.38 = 0.66.
• c. Calculate P(A∫B). Since A and B are mutually exclusive, P(A∫B) is undefined because B cannot occur if A has occured. In a mutually exclusive situation, the probability of event A given event B has occurred is 0.

For the second scenario where A and B are independent events with P(A)=0.42 and P(B)=0.52:

• a. Calculate P(A∩B). For independent events, P(A∩B) = P(A) * P(B), which is 0.42 * 0.52 = 0.2184 rounded to 0.22.
• b. Calculate P((A∪B)c). The probability of neither A nor B occurring is 1 - P(A∪B), which is 1 - (P(A) + P(B) - P(A∩B)). Calculating gives 1 - (0.42 + 0.52 - 0.2184) = 0.2984 rounded to 0.30.
• c. Calculate P(A∫B). For independent events, P(A∫B) = P(A), so the probability of A given B is 0.42.