Question

If

P(A)=0.31,
P(B)=0.44, and
P(A∩B)=0.16, find
P(B∣A). Round your answer to two decimal places.

Options:
a. 0.52
b. 0.61
c. 0.71
d. 0.84

Answer 1

To calculate P(B|A), we use the formula P(B|A) = P(A ∩ B) / P(A). Given P(A) = 0.31 and P(A ∩ B) = 0.16, we find P(B|A) = 0.16 / 0.31, which results in 0.5161, and when rounded to two decimal places gives us P(B|A) = 0.52, corresponding to option (a).

Step-by-step explanation:

To find the probability of event B given that event A has occurred, denoted as P(B|A), we use the formula:

P(B|A) = P(A ∩ B) / P(A)

Given that P(A) = 0.31 and P(A ∩ B) = 0.16, we can substitute these values into the formula:

P(B|A) = 0.16 / 0.31

We then calculate the quotient to get the conditional probability:

P(B|A) = 0.5161 (rounded to four decimal places for accuracy during calculation)

Round off the result to two decimal places:

P(B|A) = 0.52

So, the correct answer is option (a).