Question

Of the 74 people who answered "yes" to a question, 15 were male. Of the 71 people that answered "no" to the question, 6 were male. If one person is selected at random from the group, what is the probability that the person answered "yes" or was male?

Answer 1

55.2%

Explanation:

We have that 74 people answered yes and 71 answered no. So the total number of people who answered the question was 74 + 71 = 145.

Now, of those 145, 74 answering yes, then the probability of saying yes is:

P (Y) = 74/145

We know that 21 (15 + 6) are men, therefore the probability of being a man is:

P (M) = 21/145

Finally, we also know how many people answering that yes, they are men, they are 15, therefore the probability is:

P (Y and M) = 15/145

Finally, we use the "sieve" formula, for the probability that he is a man or that he answered yes.

P (Y or M) = P (Y) + P (M) - P (Y and M)

Replacing we have:

P (Y or M) = 74/145 + 21/145 - 15/145

P (Y or M) = 80/145

P (Y or M) = 0.552

In other words, the probability is 55.2%