Question

Вычислите вероятность пересечения событий A и B если а)P(A)=0,8;P(B)=0,6;P(A U B)=0,9 б)P(A)=0,5;P(B)=0,6;P(A U B)=0,8

Answer 1

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Answer 2

Calculation of the Probability of Intersection of Events A and B

To calculate the probability of the intersection of events A and B, we need to use the formula:

P(A ∩ B) = P(A) + P(B) - P(A U B)

Let's calculate the probability of the intersection of events A and B for the given scenarios:

a) P(A) = 0.8, P(B) = 0.6, P(A U B) = 0.9

Using the formula, we have:

P(A ∩ B) = P(A) + P(B) - P(A U B) = 0.8 + 0.6 - 0.9 = 0.5

Therefore, the probability of the intersection of events A and B in scenario a) is 0.5.

b) P(A) = 0.5, P(B) = 0.6, P(A U B) = 0.8

Using the formula, we have:

P(A ∩ B) = P(A) + P(B) - P(A U B) = 0.5 + 0.6 - 0.8 = 0.3

Therefore, the probability of the intersection of events A and B in scenario b) is 0.3.

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