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pollsters are concerned about declining levels of cooperation among persons contacted in surveys. a pollster contacts 77 people in the 18-21 age bracket and finds that 65 of them respond and 12 refuse to respond. when 294 people in the 22-29 age bracket are contacted, 259 respond and 35 refuse to respond. assume that 1 of the 371 people is randomly selected. find the probability of getting someone in the 22-29 age bracket or someone who agreed to respond.

Answer :

The probability of getting someone in the 22-29 age group to respond or someone who agreed to respond is 259/371

Let X be the event of contacting the 18-21 age group

Let Y be the event of contacting 22-29 age group

Let A be th event that the pollster responded

Let B be the event that they did not respond

Here,

Probability  no. of favorable outcomes/total no. of outcomes/

Hence,

n(A) = 65 + 259

= 324

P(A) = 324/371

Similarly, P(Y) = 294/371

Now,

P(A∩Y) = 259/371

We know that P(C ∪ D) = P(C) + P(D) - P(C∩D)

Therefore, P(A∪Y) = P(A) + P(Y) - P(A ∩ Y)

= 324/371 + 294/371 - 259/371

= 359/371

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