Given P(A) = 0.6 and P(B) = 0.4, do the following.(a) If A and B are independent events, compute P(A and B).(b) If P(A | B) = 0.1, compute P(A and B).
Question
Given the following probabilities:
- P(A) = 0.6
- P(B) = 0.4
Do the following:
(a) If A and B are independent events, compute P(A and B).
(b) If P(A | B) = 0.1, compute P(A and B).
Solution
(a) If A and B are independent events, the probability of both events occurring is the product of the probabilities of each event. This is expressed as P(A and B) = P(A) * P(B). Substituting the given values:
P(A and B) = 0.6 * 0.4 = 0.24
(b) If P(A | B) is given, this represents the probability of event A given that event B has occurred. The probability of both events A and B occurring is given by P(A and B) = P(A | B) * P(B). Substituting the given values:
P(A and B) = 0.1 * 0.4 = 0.04
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