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Answer :
- Define events: A (weighs 120 lb), B (consumes 2000-2500 calories).
- Calculate the conditional probability: $P(A|B) = \frac{{P(A \text{{ and }} B)}}{{P(B)}}$.
- Extract values from the table: $P(A \text{{ and }} B) = 10$, $P(B) = 110$.
- Compute the probability: $P(A|B) = \frac{{10}}{{110}} = \frac{{1}}{{11}} \approx 0.09$. The answer is $\boxed{0.09}$.
### Explanation
1. Understand the problem
We are given a two-way table that shows the distribution of people by weight and calorie consumption. We want to find the probability that a person weighs 120 pounds, given that they consume 2000 to 2500 calories per day. This is a conditional probability problem.
2. Define events and conditional probability
Let A be the event that a person weighs 120 pounds.
Let B be the event that a person consumes 2000 to 2500 calories per day.
We want to find P(A|B), which is the probability of A given B.
P(A|B) = P(A and B) / P(B).
3. Extract data from the table
From the table, the number of people who weigh 120 lb and consume 2000-2500 calories is 10.
The total number of people who consume 2000-2500 calories is 110.
4. Calculate the conditional probability
P(A|B) = (Number of people who weigh 120 lb and consume 2000-2500 calories) / (Total number of people who consume 2000-2500 calories) = 10 / 110 = 1/11.
5. Find the closest answer
1/11 is approximately 0.0909. Looking at the answer choices, the closest value is 0.09.
### Examples
Conditional probability is used in many real-world scenarios, such as medical diagnosis, risk assessment, and marketing. For example, a doctor might use conditional probability to determine the probability that a patient has a certain disease, given that the patient has certain symptoms. In marketing, conditional probability can be used to determine the probability that a customer will buy a product, given that the customer has certain characteristics.
- Calculate the conditional probability: $P(A|B) = \frac{{P(A \text{{ and }} B)}}{{P(B)}}$.
- Extract values from the table: $P(A \text{{ and }} B) = 10$, $P(B) = 110$.
- Compute the probability: $P(A|B) = \frac{{10}}{{110}} = \frac{{1}}{{11}} \approx 0.09$. The answer is $\boxed{0.09}$.
### Explanation
1. Understand the problem
We are given a two-way table that shows the distribution of people by weight and calorie consumption. We want to find the probability that a person weighs 120 pounds, given that they consume 2000 to 2500 calories per day. This is a conditional probability problem.
2. Define events and conditional probability
Let A be the event that a person weighs 120 pounds.
Let B be the event that a person consumes 2000 to 2500 calories per day.
We want to find P(A|B), which is the probability of A given B.
P(A|B) = P(A and B) / P(B).
3. Extract data from the table
From the table, the number of people who weigh 120 lb and consume 2000-2500 calories is 10.
The total number of people who consume 2000-2500 calories is 110.
4. Calculate the conditional probability
P(A|B) = (Number of people who weigh 120 lb and consume 2000-2500 calories) / (Total number of people who consume 2000-2500 calories) = 10 / 110 = 1/11.
5. Find the closest answer
1/11 is approximately 0.0909. Looking at the answer choices, the closest value is 0.09.
### Examples
Conditional probability is used in many real-world scenarios, such as medical diagnosis, risk assessment, and marketing. For example, a doctor might use conditional probability to determine the probability that a patient has a certain disease, given that the patient has certain symptoms. In marketing, conditional probability can be used to determine the probability that a customer will buy a product, given that the customer has certain characteristics.
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