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 plus Start Fraction 47 over 99 End Fraction

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

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

Answer 1

To find the conditional probability \( P(\text{brown} | \text{black}) \), we can use the formula:

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

In this scenario, let \( A \) be the event of picking a brown pair of shoes and \( B \) be the event of picking a black pair of shoes.

However, since the two events (picking a brown pair and picking a black pair) are mutually exclusive (you can't select a pair that is brown if you've already selected one that is black), we can state that:

\[
P(brown | black) = 0
\]

However, since the provided responses suggest a misunderstanding of conditional probabilities, it seems they want to consider the fractions based on the selection of shoes without overlap.

If you were to consider \( P(brown | black) \) in terms of proportions from a set of selections without repeat (which doesn't typically reflect conditional probabilities accurately):

- The total number of shoes is \( 100 \).
- The fraction of brown shoes is \( \frac{26}{100} \).
- The fraction of black shoes is \( \frac{47}{100} \).

Thus, the most reasonable response from the selections provided aligns with the direct consideration of the proportion, which is:

\[
\frac{26}{100}
\]

None of the given responses mention a correct answer for zero or considering mutually exclusive outcomes. So, the best response that reflects information derived from the initial question is:

\[
\frac{26}{100}
\]

Thus, the correct answer is:

**Start Fraction 26 over 100 End Fraction**