Question

If p(a) = 0.2, p(b|a) = 0.25, p(a ∪ b) = 0.67, find p(b).

Answer 1

To find P(B), the formula P(A ∪ B) = P(A) + P(B) - P(A and B) is used. P(A and B) is calculated as P(B|A) × P(A), which is 0.25 × 0.2 = 0.05. Then, P(B) is found to be 0.52 by rearranging the formula.

Step-by-step explanation:

The question is asking to find the probability of event B, P(B). We are given:

• P(A) = 0.2
• P(B|A) = 0.25
• P(A ∪ B) = 0.67

Using the formula for the probability of the union of two events:

P(A ∪ B) = P(A) + P(B) - P(A and B)

Given P(B|A) is the probability of B given A, we can find P(A and B):

P(A and B) = P(B|A) × P(A) = 0.25 × 0.2 = 0.05

Now, we can use this to find P(B):

P(B) = P(A ∪ B) + P(A and B) - P(A) = 0.67 + 0.05 - 0.2 = 0.52

So, the probability of event B, P(B), is 0.52.