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

Answer:

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

Step-by-step 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

$P = \frac{P_{FN}}{P_{N}} = \frac{0.2272}{0.608} = 0.3737$

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