Question

A and B are two events of an experiment. P((A cup B)^ prime )= 0 * 39 , P(A cap B)= 0 - 1 and P( B backslash A)=2P(A backslash B).

Find P(B)

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Answer 1

Answer: P(B) is equal to 0.39.

Explanation:

To find P(B), we can use the complement rule and the formula for the probability of the union of two events.

1. P((A ∪ B)') = 1 - P(A ∪ B)

Since (A ∪ B)' represents the complement of (A ∪ B), we can rewrite the equation as:

1 - P(A ∪ B) = 0.39

2. P(A ∩ B) = 0 - 1

Since the given value is negative, we can rewrite it as:

P(A ∩ B) = -1

3. P(B \ A) = 2P(A \ B)

This equation tells us that the probability of B occurring without A is twice the probability of A occurring without B.

Using these equations, we can solve for P(B).

Let's start with equation 3:

P(B \ A) = 2P(A \ B)

Since P(A \ B) represents the probability of A occurring without B, and P(B \ A) represents the probability of B occurring without A, we can rewrite equation 3 as:

P(B) = 2P(A \ B)

Now, let's substitute this expression for P(B) into equation 1:

1 - P(A ∪ B) = 0.39

Substituting P(B) = 2P(A \ B):

1 - (P(A) + P(B) - P(A ∩ B)) = 0.39

Substituting P(A ∩ B) = -1 and rearranging the equation:

1 - (P(A) + 2P(A \ B) + 1) = 0.39

Simplifying the equation:

-2P(A \ B) = -0.39

Dividing both sides by -2:

P(A \ B) = 0.39/2

P(A \ B) = 0.195

Now, substituting this value back into P(B) = 2P(A \ B):

P(B) = 2 * 0.195

P(B) = 0.39