Question

pollsters are concerned about declining levels of cooperation among persons contacted in surveys. a pollster contacts 79 people in the 18 - 21 age bracket and finds that 67 of them respond and 12 refuse to respond. when 263 people in the 22 - 29 age bracket are contacted, 240 respond and 23 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 does not respond. report the answer as a percent rounded to one decimal place accuracy. you need not enter the % symbol. p(22 - 29 or does not respond) = % (hint: it might be helpful to organize the data into a table first.)

Explanation:

Step1: Calculate number of non - responders

The number of non - responders in the 18 - 21 age bracket is 12, and in the 22 - 29 age bracket is 23. So the total number of non - responders is $12 + 23=35$.
The total number of people in the 22 - 29 age bracket is 263.
The total number of people surveyed is 342.

Step2: Use the formula for the probability of the union of two events

The formula for $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Let $A$ be the event of being in the 22 - 29 age bracket and $B$ be the event of not responding.
$P(A)=\frac{263}{342}$, $P(B)=\frac{35}{342}$, and $P(A\cap B)=\frac{23}{342}$.
$P(A\cup B)=\frac{263 + 35-23}{342}=\frac{275}{342}$.

Step3: Convert to percentage

$P=\frac{275}{342}\times100\approx80.4\%$

Answer:

80.4