Question

The probability of a student being on the debate team is .42. The probability of him being on the math team is .26. The probability that he is on both teams is .20.
What is the probability his is on the math team if we know he is on the debate team?

.48

.42

.66

.77

Answer 1

It is given that probability of a student being on the debate team is 0.42

So, P(D) = 0.42

It is given that probability of a student being on the math team is 0.26

So, P(M)= 0.26

The probability that he is on both teams is .20

So, $P(D\cap M)=0.20$

We have to determine the probability his is on the math team if we know he is on the debate team. This is the case of conditional probability.

So, $P(M/D)=\frac{P(D\cap M)}{P(D)}$

$P(M/D)=\frac{0.20}{0.42}$

= 0.476

= 0.48

Therefore, the probability that he is on the math team if we know he is on the debate team is 0.48.

Option 1 is the correct answer.