Question

Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 80 people in the​ 18-21 age bracket and finds that 49 of them respond and 31 refuse to respond. When 286 people in the​ 22-29 age bracket are​ contacted, 261 respond and 25 refuse to respond. Suppose that one of the 366 people is randomly selected. Find the probability of getting someone in the 18 dash 21 age bracket or someone who refused to respond.

Answer 1

0.3716

Explanation:

"OR" means "+" and "AND" means "*"

This is true for probability problems like this.

We want "the probability of getting someone in the 18 dash 21 age bracket or someone who refused to respond."

We need the probability of getting someone in the 18 dash 21 age bracket

We also need the probability someone who refused to respond

Then ADD both, [since "OR"]

Now,

Out of 366 people, 80 are from 18-21 bracket, so

the probability of getting someone in the 18 dash 21 age bracket = 80/366

Also,

Out of 366 people, (31+25)=56 refuse to respond

the probability someone who refused to respond = 56/366

the probability of getting someone in the 18 dash 21 age bracket or someone who refused to respond = 80/366 + 56/366 = 136/366 = 0.3716