Question

Find the missing probability.

[ P(A cap B) ]
Given ( P(A|B) = 20 ) and ( P(B) = 50 ).
a) 10
b) 20
c) 25
d) 50

Answer 1

The missing probability P(A ∩ B) is found by multiplying the conditional probability P(A|B) by the probability P(B), resulting in a probability of 10% (option a).

Step-by-step explanation:

The student needs to find the missing probability P(A ∩ B), given P(A|B) = 0.20 (20%) and P(B) = 0.50 (50%). The formula to find the joint probability P(A ∩ B) from the conditional probability P(A|B) is:

P(A ∩ B) = P(A|B) × P(B)

Using the given values, we calculate the joint probability as follows:

P(A ∩ B) = 0.20 × 0.50 = 0.10

Therefore, the correct answer is a) 10%.