Answer :
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]
[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]