Question

Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 98 people in the 18-21 age bracket and finds that 83 of them respond and 15 refuse to respond. When 244 people in the 22-29 age bracket are contacted, 227 respond and 17 refuse to respond. Assume that 1 of the 342 people is randomly selected. Find the probability of getting someone in the 22-29 age bracket or someone who refused to respond.

Give your answer as a decimal (to at least 4 places).

Answer 1

Out of 342 people, 244 belong to the age bracket of 22-29.

Out of 342 people, 32 refused to respond.

17 people in the age bracket of 22-29 refused to respond.

Let A be the event of getting someone in the 22-29 age bracket and B be the event of selecting someone who refused to respond.

P(A) = 244/342 = 0.7135, P(B) = 0.0936, P(A B) = 17/342 = 0.0497

Thus, the probability of getting someone in the 22-29 age bracket or someone who refused to respond = P(A B) = P(A) + P(B) - P(A B) = 0.7135 + 0.0936 - 0.0497 = 0.7574