Question

The probability of event A occurring given that event B has already occurred is 0.61. The probability of both events occurring is 0.5. What is the probability of event B occurring?

Answer 1

P(B)= 0.305

Explanation:

Hello!

This exercise is an application of conditional probabilities.

You know that the definition of a conditional probability is:

`P(A/B) = (P(AnB))/(P(B))`

And

The probability of A occuring, given that B has already ocurred is P(A/B)= 0.61

The probability of A and B ocurring at the same time is P(A∩B)= 0.5

You can clear the probability of B from the equation:

P(B)= P(A/B)*P(A∩B)= 0.61*0.5= 0.305

I hope you have a SUPER day!