High School

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Select the correct answer.

\[
\begin{array}{|c|c|c|c|c|}
\hline
\text{Weight/Calories per Day} & \text{1000 to 1500 cal.} & \text{1500 to 2000 cal.} & \text{2000 to 2500 cal.} & \text{Total} \\
\hline
\text{120 lb.} & 90 & 80 & 10 & 180 \\
\hline
\text{145 lb.} & 35 & 143 & 25 & 203 \\
\hline
\text{165 lb.} & 15 & 27 & 75 & 117 \\
\hline
\text{Total} & 140 & 250 & 110 & 500 \\
\hline
\end{array}
\]

Based on the data in the two-way table, what is the probability that a person weighs 120 pounds, given that he or she consumes 2,000 to 2,500 calories per day?

A. 0.09
B. 0.12
C. 0.22
D. 0.35

Answer :

To solve this problem, we need to determine the probability that a person weighs 120 pounds, given that they consume 2,000 to 2,500 calories per day.

Here's how you can find this probability step-by-step:

1. Identify the Relevant Data:
- From the table, find the number of people who weigh 120 pounds and consume 2,000 to 2,500 calories per day. According to the table, this number is 10.

2. Total People in the Specified Category:
- Look at the total number of people who consume 2,000 to 2,500 calories per day, regardless of their weight. From the table, this total is 110.

3. Calculate the Conditional Probability:
- The probability we are seeking is the number of 120-pound individuals who consume 2,000 to 2,500 calories per day divided by the total number of people who consume this amount of calories.
- Mathematically, this is expressed as:
[tex]\[
\text{Probability} = \frac{\text{Number of 120 lb individuals consuming 2000-2500 cal}}{\text{Total number of individuals consuming 2000-2500 cal}}
\][/tex]
- Substituting the numbers from the table:
[tex]\[
\text{Probability} = \frac{10}{110} = \frac{1}{11} \approx 0.0909
\][/tex]

4. Select the Closest Answer:
- Looking at the given choices, the probability [tex]\(\approx 0.0909\)[/tex] corresponds to 0.09.

Therefore, the correct answer is A. 0.09.

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