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Question
Let A and B be independent events with P (A) = 0.3 and P (B) = 0.4. Find
- P (A ∩ B)
- P (A ∪ B)
- P (A | B)
- P (B | A)
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Solution
It is given that P (A) = 0.3 and P (B) = 0.4
If A and B are independent events, then
(i) P(A ∩ B) = P(A) · P(B)
P(A ∩ B) = 0.3 × 0.4
P(A ∩ B) = 0.12
(ii) P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
P(A ∪ B) = 0.3 + 0.4 - 0.12
P(A ∪ B) = 0.58
(iii) P(A | B) = `(P(A ∩ B))/(P(B))`
P(A | B) = `0.12/0.4`
P(A | B) `= 3/10`
P(A | B) `= 0.3`
(iv) P(B | A) = `(P(A ∩ B))/(P(A))`
P(B | A) = `0.12/0.3`
P(B | A) = 0.4
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