A survey is conducted to study the favorite sport of individuals in different age groups. The two-way table is given below:
| | Football | Basketball | Baseball | Total |
| :-------------------- | :------- | :--------- | :------- | :---- |
| $8 - 12 ~ yrs$ | 10 | 12 | 10 | $32$ |
| $13 - 17 ~ yrs$ | 8 | 6 | 24 | $38$ |
| $18 - 22 ~ yrs$ | 16 | 2 | 12 | $30$ |
| Total | $34$ | $20$ | $46$ | $100$ |
What is the probability that a randomly selected person from this survey's favorite sport is basketball, given they are 18 to 22 years old?
$P(\text{Basketball} \mid 18-22 yrs) = [?] \%$
Round your answer to the nearest whole percent.
Answer (2)
Find the number of people aged 18-22 who prefer basketball: 2.
Find the total number of people aged 18-22: 30.
Calculate the conditional probability: 30 2 = 15 1 .
Convert to percentage and round: 15 1 × 100 ≈ 7 % .
Explanation
Understand the problem We are given a two-way table that shows the favorite sport of individuals in different age groups. We want to find the probability that a randomly selected person's favorite sport is basketball, given that they are in the 18-22 age group.
Identify the relevant numbers From the table, we can see that there are 2 people in the 18-22 age group who prefer basketball. The total number of people in the 18-22 age group is 30.
Calculate the conditional probability To calculate the conditional probability, we use the formula: P ( " B a s k e t ba ll "∣"18 − 22 yrs " ) = Total number of people aged 18-22 Number of people aged 18-22 who prefer basketball Plugging in the values, we get: P ( " B a s k e t ba ll "∣"18 − 22 yrs " ) = 30 2 = 15 1
Convert to percentage Now, we convert this probability to a percentage by multiplying by 100: 15 1 × 100 = 6.666...
Round to the nearest whole percent Finally, we round the percentage to the nearest whole percent, which is 7%.
State the final answer Therefore, the probability that a randomly selected person's favorite sport is basketball, given they are 18 to 22 years old, is 7%.
Examples
Imagine you're organizing a sports event for different age groups and want to understand the preferences of the 18-22 age group. Knowing the probability that someone in this group prefers basketball helps you allocate resources and plan activities accordingly. For instance, if you know that about 7% of this age group prefers basketball, you can ensure you have enough basketball-related activities to cater to their interests.
The probability that a randomly selected person's favorite sport is basketball, given they are 18 to 22 years old, is 7%. This was calculated using the number of people in that age group who prefer basketball and the total number of people in the same age group. Thus, the final answer is 7%.
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