To find the probability that a person weighs 120 pounds given that they consume 2000 to 2500 calories per day, we can use the concept of conditional probability. The formula for conditional probability is:
[tex]\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \][/tex]
In this problem:
- [tex]\( A \)[/tex] is the event that a person weighs 120 pounds.
- [tex]\( B \)[/tex] is the event that a person consumes 2000 to 2500 calories per day.
From the given data:
- The total number of people consuming 2000 to 2500 calories per day is 110.
- The number of people who weigh 120 pounds and consume 2000 to 2500 calories per day is 10.
So, the probability that a person weighs 120 pounds given that they consume 2000 to 2500 calories per day is calculated as:
[tex]\[ P(\text{120 lb} | \text{2000 to 2500 cal}) = \frac{\text{Number of people who weigh 120 lb and consume 2000 to 2500 cal}}{\text{Total number of people who consume 2000 to 2500 cal}} \][/tex]
[tex]\[ P(\text{120 lb} | \text{2000 to 2500 cal}) = \frac{10}{110} \][/tex]
Upon simplifying this fraction, we get approximately [tex]\( 0.0909 \)[/tex]. Therefore, the correct answer to the question is:
A. 0.09
