Question

Mr. Jay has 100 pairs of shoes in his closet. He has 26 brown pairs, 12 navy pairs, 47 black pairs, and 15 white pairs. What is P(brown|black)
?(1 point)
Responses

26100
Start Fraction 26 over 100 End Fraction

26100⋅4799
Start Fraction 26 over 100 End Fraction times Start Fraction 47 over 99 End Fraction

26100+4799
Start Fraction 26 over 100 End Fraction plus Start Fraction 47 over 99 End Fraction

26100⋅47100
Start Fraction 26 over 100 End Fraction times Start Fraction 47 over 100 End Fraction
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Answer 1

To find \( P(\text{brown} | \text{black}) \), which is the probability of selecting a brown pair of shoes given that a black pair of shoes has been selected, we need to use the formula for conditional probability:

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

In this case, let:
- \( A \) be the event of selecting a brown pair of shoes.
- \( B \) be the event of selecting a black pair of shoes.

However, since selecting a black pair of shoes means we already have one pair of shoes out of the total, the probability \( P(A|B) = P(\text{brown}) \) in this case is straightforward since after the condition does not affect the pair count of brown shoes in this context.

Since \( P(\text{brown}) \) is simply the ratio of brown pairs to total pairs:

\[
P(\text{brown}) = \frac{\text{Number of brown pairs}}{\text{Total pairs}} = \frac{26}{100}
\]

Thus, since we're effectively looking for brown pairs when we are not further restricting our selection (except that we are choosing from pairs overall):

The answer is \( \frac{26}{100} \).

So the correct response is:

\(\text{Start Fraction 26 over 100 End Fraction}\)