Given P(A) = 0.4, P(B) = 0.5, P(A | B) = 0.3, do the following.(a) Compute P(A and B). (b) Compute P(A or B).
Question
Given:
- P(A) = 0.4
- P(B) = 0.5
- P(A | B) = 0.3
Tasks:
(a) Compute P(A and B).
(b) Compute P(A or B).
Solution
(a) To compute P(A and B), we use the formula for conditional probability, which is P(A and B) = P(A | B) * P(B). Substituting the given values, we get P(A and B) = 0.3 * 0.5 = 0.15.
(b) To compute P(A or B), we use the formula P(A or B) = P(A) + P(B) - P(A and B). Substituting the given values, we get P(A or B) = 0.4 + 0.5 - 0.15 = 0.75.
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