# Solved: The table below summarizes results from a study of people who refused to answer survey questions. Use the table to

#### ByDr. Raju Chaudhari

Oct 12, 2020

The table below summarizes results from a study of people who refused to answer survey questions. Use the table to answer the following questions. Be very careful to read the question carefully to determine whether or not there is overlap.

Age 18-21 22-29 30-39 40-49 50-59 60 and over
Responded 70 252 242 133 135 199
Refused 13 22 35 28 37 59

If one of the subjects is randomly selected, what is the probability that a randomly selected person is between 22 and 29 years or refused to answer?

The probability that a randomly selected person is between 22 and 29 years or refused to answer is _____

(Do not round until the final answer. Then round to three decimal places as needed.

If one of the subjects is randomly selected, what is the probability that the selected person was between 16 and 21 years or refused to answer?

The probability that the selected person was between 18 and 21 year or refused to answer is _____

(Do not round until the final answer. Then round to three decimal places as needed.)

### Solution

Age 18-21 22-29 30-39 40-49 50-59 60 and over
Responded 70 252 242 133 135 199
Refused 13 22 35 28 37 59

Let $A$ denote person is between 22 and 29, $B$ denote denote the person refused to answer.

$P(A) = \frac{274}{1225}$, $P(B) = \frac{194}{1225}$ and $P(A\cap B) =\frac{22}{1225}$.

The probability that the selected person was between 22 and 29 year or refused to answer is $P(A\cup B)$

 \begin{aligned} P(A\cup B) &= P(A) + P(B) - P(A\cap B)\\ &= \frac{274}{1225} + \frac{194}{1225} - \frac{22}{1225}\\ &= 0.364 \end{aligned}
The probability that a randomly selected person is between 22 and 29 years or refused to answer is 0.364

Let $C$ denote person is between 18 and 21, $D$ denote denote the person refused to answer.

$P(C) = \frac{83}{1225}$, $P(D) = \frac{194}{1225}$ and $P(C\cap D) =\frac{13}{1225}$.

The probability that the selected person was between 18 and 21 year or refused to answer is $P(C\cup D)$

 \begin{aligned} P(C\cup D) &= P(C) + P(D) - P(C\cap D)\\ &= \frac{83}{1225} + \frac{194}{1225} - \frac{13}{1225}\\ &= 0.216 \end{aligned}
The probability that a randomly selected person is between 18 and 21 years or refused to answer is 0.216