Question

In the Legal Eagle law firm, 68% of the lawyers are male while 32% are female. Of the male lawyers, 44% are corporate lawyers and 56% are non-corporate lawyers. Of the female lawyers, 29% are corporate lawyers and 71% are non-corporate lawyers. If a lawyer is chosen at random and they are not a corporate lawyer, calculate the probability that they are female. Give your answer as a decimal to 2 decimal places. Probability = Submit answers Bookmark

Answer 1

thirty-seven percent chance

Explanation:

Answer 2

If a lawyer is chosen at random and they are not a corporate lawyer, there is a 37.37% probability that they are female.

Explanation:

In this problem, we have these following probabilities:

A 68% probability that the lawyer is male.

A 32% probability that the lawyer is female.

If he is a male, a 44% probability that he is a corporate lawyer and a 56% probability that he is not a corporate lawyer.

If she is female, a 29% probability that she is a corporate lawyer and a 71% probability that she is not a corporate lawyer.

If a lawyer is chosen at random and they are not a corporate lawyer, calculate the probability that they are female.

This is the probability that a lawyer is female and a non corporate lawyer divided by the probability that a lawyer is not a corporate lawyer.

Probability that a lawyer is a non-corporate lawyer.

68% of the lawyers are male. Of those, 56% are non corporate.

32% of the lawyers are female. Of those, 71% are non corporate.

So:

`P_(N) = 0.68*(0.56) + 0.32*(0.71) = 0.608`

Probability that a lawyer is a female and non-corporate:

32% of the lawyers are female. Of those, 71% are non corporate.

`P_(FN) = 0.32*(0.71) = 0.2272`

Finally

`P = (P_(FN))/(P_(N)) = (0.2272)/(0.608) = 0.3737`

If a lawyer is chosen at random and they are not a corporate lawyer, there is a 37.37% probability that they are female.