Question

video lesson 5.3 example 4 - finding conditional probabilities
a store surveys customers of different ages. the survey asks whether they would
like to see the store expand its toy department. the results, given as joint
relative frequencies, are shown in the two - way table.

1. what is the probability that a randomly selected

customer whose age is between 10 and 20 would not
like to see the toy department expanded?

	age (in years)	age (in years)	age (in years)
yes	0.27	0.06	0.23
no	0.09	0.17	0.18

Explanation:

Step1: Identify relevant data

For age 10 - 20, "Yes" frequency is 0.06, "No" frequency is 0.17. Total for 10 - 20: \(0.06 + 0.17 = 0.23\).

Step2: Calculate conditional probability

Conditional probability \(P(\text{No} | 10 - 20)=\frac{P(\text{No and } 10 - 20)}{P(10 - 20)}=\frac{0.17}{0.06 + 0.17}=\frac{0.17}{0.23}\approx0.739\) (or keep as fraction \(\frac{17}{23}\)).

Answer:

\(\frac{17}{23}\) (or approximately \(0.739\))