Question

if P(B')=0.65, P(A U B)=0.85 and A and B are independent events, then P(A) = ​

Answer 1

Answer:

0.5

Step-by-step explanation:

Given :

P(B')=0.65, P(A U B)=0.85

A and B are independent events

To find :

P(A)

Formulae used :

P(X') = 1 - P(X)

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Solution :

We know that if A and B are independent then P(A ∩ B) = 0

From the formula (1)

P(B) = 1 - P(B')

P(B) = 1 - 0.65

P(B) = 0.35

Now, from addition theorem of probability using formula (2), we get,

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

=> 0.85 = P(A) + 0.35 - 0

=> P(A) = 0.85 - 0.35

=> P(A) = 0.5

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