Question

The probability that Joanne has eggs for breakfast and goes to school by car is 0.4 The probability that she goes ta school by car on any day is 0.5
What is the probability that Joanne has had eggs for breakfast if she went to school by car?
A. 0.1
C
B.
0.2
C.
0.4
D.
0.5
E.
0.8

Answer 1

To find the probability that Joanne had eggs for breakfast given that she went to school by car, we can use Bayes' theorem. We are given the following probabilities:

- \( P(A \cap B) = 0.4 \), where \( A \) is the event that Joanne has eggs for breakfast and \( B \) is the event that she goes to school by car.
- \( P(B) = 0.5 \).

We want to find \( P(A|B) \), the probability that Joanne had eggs for breakfast given that she went to school by car. By Bayes' theorem, we can express this as:

\[
P(A|B) = \frac{P(A \cap B)}{P(B)}
\]

Substituting the values we know:

\[
P(A|B) = \frac{0.4}{0.5} = 0.8
\]

Thus, the probability that Joanne had eggs for breakfast given that she went to school by car is **0.8**.

The answer is **E. 0.8**.