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?

Question

Mathematics

Lillianna Montoya

10 November, 20:26

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?

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Answers (1)

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Matias Meza · Answer 1

55.2%

Step-by-step 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%