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:
[tex]P_{N} = 0.68*(0.56) + 0.32*(0.71) = 0.608[/tex]
Probability that a lawyer is a female and non-corporate:
32% of the lawyers are female. Of those, 71% are non corporate.
[tex]P_{FN} = 0.32*(0.71) = 0.2272[/tex]
Finally
[tex]P = \frac{P_{FN}}{P_{N}} = \frac{0.2272}{0.608} = 0.3737[/tex]
If a lawyer is chosen at random and they are not a corporate lawyer, there is a 37.37% probability that they are female.
Answer:
thirty-seven percent chance
Step-by-step explanation:
