Question
At a zoo, a sampling of children was asked if the zoo were to get one additional animal, would they prefer a lion or
an elephant. The results of the survey follow:
If one child who was in the survey is selected at random, find the probability that
21) The child selected the lion, given the child is a girl.
22) The child is a boy, given the child preferred the elephant.
23) The child selected is a girl, given that the child preferred the lion.
24) The child preferred the elephant given they are a girl
an elephant. The results of the survey follow:
If one child who was in the survey is selected at random, find the probability that
21) The child selected the lion, given the child is a girl.
22) The child is a boy, given the child preferred the elephant.
23) The child selected is a girl, given that the child preferred the lion.
24) The child preferred the elephant given they are a girl
Answers
GPT-4o mini
To answer your questions about probabilities, we would need the specifics of the survey results, such as how many boys and girls preferred the lion or the elephant. Unfortunately, the data hasn’t been provided.
However, I can provide you with a general method for how to approach each of these probability questions using the following notation:
- Let \( L \) be the event that a child prefers a lion.
- Let \( E \) be the event that a child prefers an elephant.
- Let \( G \) be the event that the child is a girl.
- Let \( B \) be the event that the child is a boy.
The probabilities can be calculated as follows, given that you can input the actual counts from your survey:
### 1. Probability that the child selected the lion, given the child is a girl:
This is expressed as \( P(L | G) \) and can be calculated as:
\[
P(L | G) = \frac{P(L \cap G)}{P(G)}
\]
Where:
- \( P(L \cap G) \) is the number of girls who preferred the lion divided by the total number of children surveyed.
- \( P(G) \) is the total number of girls surveyed divided by the total number of children surveyed.
### 2. Probability that the child is a boy, given the child preferred the elephant:
This is expressed as \( P(B | E) \) and can be calculated as:
\[
P(B | E) = \frac{P(B \cap E)}{P(E)}
\]
Where:
- \( P(B \cap E) \) is the number of boys who preferred the elephant divided by the total number of children surveyed.
- \( P(E) \) is the total number of children who preferred the elephant divided by the total number of children surveyed.
### 3. Probability that the child selected is a girl, given the child preferred the lion:
This is expressed as \( P(G | L) \) and can be calculated as:
\[
P(G | L) = \frac{P(G \cap L)}{P(L)}
\]
Where:
- \( P(G \cap L) \) is the number of girls who preferred the lion divided by the total number of children surveyed.
- \( P(L) \) is the total number of children who preferred the lion divided by the total number of children surveyed.
### 4. Probability that the child preferred the elephant given they are a girl:
This is expressed as \( P(E | G) \) and can be calculated as:
\[
P(E | G) = \frac{P(E \cap G)}{P(G)}
\]
Where:
- \( P(E \cap G) \) is the number of girls who preferred the elephant divided by the total number of children surveyed.
- \( P(G) \) is the total number of girls surveyed divided by the total number of children surveyed.
If you can provide the specific counts from the survey, I can help you compute these probabilities directly!
However, I can provide you with a general method for how to approach each of these probability questions using the following notation:
- Let \( L \) be the event that a child prefers a lion.
- Let \( E \) be the event that a child prefers an elephant.
- Let \( G \) be the event that the child is a girl.
- Let \( B \) be the event that the child is a boy.
The probabilities can be calculated as follows, given that you can input the actual counts from your survey:
### 1. Probability that the child selected the lion, given the child is a girl:
This is expressed as \( P(L | G) \) and can be calculated as:
\[
P(L | G) = \frac{P(L \cap G)}{P(G)}
\]
Where:
- \( P(L \cap G) \) is the number of girls who preferred the lion divided by the total number of children surveyed.
- \( P(G) \) is the total number of girls surveyed divided by the total number of children surveyed.
### 2. Probability that the child is a boy, given the child preferred the elephant:
This is expressed as \( P(B | E) \) and can be calculated as:
\[
P(B | E) = \frac{P(B \cap E)}{P(E)}
\]
Where:
- \( P(B \cap E) \) is the number of boys who preferred the elephant divided by the total number of children surveyed.
- \( P(E) \) is the total number of children who preferred the elephant divided by the total number of children surveyed.
### 3. Probability that the child selected is a girl, given the child preferred the lion:
This is expressed as \( P(G | L) \) and can be calculated as:
\[
P(G | L) = \frac{P(G \cap L)}{P(L)}
\]
Where:
- \( P(G \cap L) \) is the number of girls who preferred the lion divided by the total number of children surveyed.
- \( P(L) \) is the total number of children who preferred the lion divided by the total number of children surveyed.
### 4. Probability that the child preferred the elephant given they are a girl:
This is expressed as \( P(E | G) \) and can be calculated as:
\[
P(E | G) = \frac{P(E \cap G)}{P(G)}
\]
Where:
- \( P(E \cap G) \) is the number of girls who preferred the elephant divided by the total number of children surveyed.
- \( P(G) \) is the total number of girls surveyed divided by the total number of children surveyed.
If you can provide the specific counts from the survey, I can help you compute these probabilities directly!