Question

Given P(A)=0.63P(A)=0.63, P(B)=0.4P(B)=0.4 and P(A\text{ and }B)=0.332P(A and B)=0.332, find the value of P(B|A)P(B∣A), rounding to the nearest thousandth, if necessary.

Answer 1

Considering the definition of conditional probability, the conditional probability P(B|A) is 0.527.

Definition of conditional probability

Probability is the greater or lesser possibility of a certain event occurring, this is, it establishes a relationship between the number of favorable events and the total number of possible events.

The conditional probability P(A|B) is the probability that event A occurs, knowing that another event B also occurs. That is, it is the probability that event A occurs if event B has occurred. It is defined as:

P(A|B) = P(A∩B)÷ P(B)

Conditional probability in this case

In this case, you know:

• P(A)= 0.63
• P(B)= 0.4
• P(A and B)= P(A∩B)= 0.332

Replacing in the definition of conditional probability:

P(B|A) = P(A∩B)÷ P(A)

P(B|A)= 0.332÷ 0.63

Solving:

P(B|A) = 0.527

Finally, the conditional probability P(B|A) is 0.527.

Answer 2

Okay, here we have this:

Considering the provided information, we are going to calculate the requested probability, so we obtain the following:

Then to find the requested conditional probability we will substitute in the following formula:

`\begin{gathered} P(B|A)=(P(A\cap B))/(P(A)) \\ =(0.332)/(0.63) \\ \approx0.53 \end{gathered}`

Finally we obtain that P(B|A) is approximately equal to 0.53.