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Question

There are declining levels of cooperation among persons contacted in surveys and this brings concerns to pollsters. A pollster contacts 81 people in the 18-21 age bracket and finds that 69 of them respond and 12 refuse to respond. When 295 people in the 22-29 age bracket are contacted, 260 respond and 35 refuse to respond. Assume that 1 of the 376 people is randomly selected. Find the probability of getting someone in the 18-21 age bracket or someone who refused to respond.

Answer 1

This is an example of the General Addition Rule for probability.

P(A U B) = P(A) + P(B) - P(A ∩ B)

In words, it's: Probability of A or B = Probability of A + Probability of B - Probability of both A and B at the same time. (Subtracting the last term avoids counting items twice.)

Here, let A be the event that the person is in 18-21 bracket, so P(A) = 81/376

and B be the event person refused to respond, so P(B) = (12 + 35)/376 = 47/376

then A ∩ B is the event that the person is in 18-21 bracket and refused to respond, so P(A ∩ B) = 12/376

Now we have all the information needed:

P(A U B) = P(A) + P(B) - P(A ∩ B) = 81/376 + 47/376 - 12/376 = 116/376 which reduces to 29/94