For two events A and B, P(A) = 0.4, P(B) = 0.7 and P(A B) = 0.2. Find P(A B)._______________________________________________________________________13 For two events A and B, P(A) = 0.4, P(B) = 0.7 and P(A B) = 0.3. Find P(A B)._______________________________________________________________________14 For two events G and H, P(G) = 0.5, P(G H) = 0.2 and P(G H) = 0.6. Find P(H).
Question
For two events A and B, P(A) = 0.4, P(B) = 0.7 and P(A B) = 0.2. Find P(A B)._______________________________________________________________________13 For two events A and B, P(A) = 0.4, P(B) = 0.7 and P(A B) = 0.3. Find P(A B)._______________________________________________________________________14 For two events G and H, P(G) = 0.5, P(G H) = 0.2 and P(G H) = 0.6. Find P(H).
Solution
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To find P(A ∪ B) for the first scenario, we use the formula P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Substituting the given values, we get P(A ∪ B) = 0.4 + 0.7 - 0.2 = 0.9.
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For the second scenario, we use the same formula. Substituting the given values, we get P(A ∪ B) = 0.4 + 0.7 - 0.3 = 0.8.
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To find P(H) for the third scenario, we use the formula P(G ∪ H) = P(G) + P(H) - P(G ∩ H). We can rearrange this formula to solve for P(H): P(H) = P(G ∪ H) - P(G) + P(G ∩ H). Substituting the given values, we get P(H) = 0.6 - 0.5 + 0.2 = 0.3.
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