Select the correct answer.

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

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. [tex]\(0.09\)[/tex]
B. [tex]\(0.12\)[/tex]
C. [tex]\(0.22\)[/tex]
D. [tex]\(0.35\)[/tex]

To find the probability that a person weighs 120 pounds, given that they consume 2,000 to 2,500 calories per day, we can use the concept of conditional probability. The formula for conditional probability is:

[tex]\[
P(A \mid B) = \frac{P(A \text{ and } B)}{P(B)}
\][/tex]

In this situation:

- [tex]\( A \)[/tex] is the event that a person weighs 120 pounds.
- [tex]\( B \)[/tex] is the event that a person consumes 2,000 to 2,500 calories per day.

From the table:

- The number of people who weigh 120 pounds and consume 2,000 to 2,500 calories per day is 10. This is the value for [tex]\( P(A \text{ and } B) \)[/tex].

- The total number of people who consume 2,000 to 2,500 calories per day is 110. This is the value for [tex]\( P(B) \)[/tex].

Therefore, the probability that a person weighs 120 pounds, given that they consume 2,000 to 2,500 calories per day, is:

[tex]\[
P(120 \text{ lb } \mid 2000 \text{ to } 2500 \text{ cal }) = \frac{10}{110}
\][/tex]

Simplifying this fraction gives approximately:

[tex]\[
\frac{10}{110} = 0.0909
\][/tex]

This rounds to approximately 0.09, so the correct answer is:

A. [tex]\( \quad 0.09 \)[/tex]