To determine the probability that a teenager has exactly 4 pairs of shoes in their closet, we can follow these steps:
1. Identify the given data:
- Pairs of Shoes: [tex]\(1, 2, 3, 4, 5\)[/tex]
- Frequency (Number of Teenagers with each respective number of pairs of shoes): [tex]\(18, 30, 57, 30, 15\)[/tex]
2. Calculate the total number of teenagers:
Sum the frequencies to find the total number of teenagers.
[tex]\[
\text{Total number of teenagers} = 18 + 30 + 57 + 30 + 15 = 150
\][/tex]
3. Find the frequency of teenagers having exactly 4 pairs of shoes:
According to the given data, the frequency of teenagers having exactly 4 pairs of shoes is:
[tex]\[
\text{Frequency of 4 pairs of shoes} = 30
\][/tex]
4. Calculate the probability ([tex]\( P(4) \)[/tex]) that a teenager has exactly 4 pairs of shoes:
The probability is the ratio of the number of teenagers who have exactly 4 pairs of shoes to the total number of teenagers.
[tex]\[
P(4) = \frac{\text{Number of teenagers with 4 pairs of shoes}}{\text{Total number of teenagers}} = \frac{30}{150}
\][/tex]
5. Simplify the fraction:
[tex]\[
P(4) = \frac{30}{150} = \frac{1}{5} = 0.2
\][/tex]
Thus, the probability that a teenager has exactly 4 pairs of shoes in their closet is:
[tex]\[
P(4) = 0.2
\][/tex]
