A survey of 4826 randomly selected young adults (aged 19 to 25) asked, “What do you think are the chances you will have much more than a middle-class income at age 30?” The two-way table summarizes the responses.

Choose a survey respondent at random. Define events G: a good chance, M: male, and N: almost no chance.

a. Find P(G | M). Interpret this value in context.

b. Given that the chosen survey respondent didn’t say “almost no chance,” what’s the probability that this person is female? Write your answer as a probability statement using correct symbols for the events.

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Gender Female Male Total Almost no 96 98 194 chance Some chance 426 286 712 but probably not Opinion A 50-50 chance 696 720 1416 A good chance 663 758 1421 Almost certain 486 597 1083 Total 2367 2459 4826