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⋅47100 Start Fraction 26 over 100 End Fraction times Start Fraction 47 over 100 End Fraction 26100⋅4799 Start Fraction 26 over 100 End Fraction times Start Fraction 47 over 99 End Fraction

Answer 1

To find \( P(\text{brown | black}) \), we need to calculate the conditional probability of selecting a brown pair of shoes given that a black pair has already been selected.

The formula for conditional probability is given by:

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

In this case:

• Let \( A \) be the event of picking a brown pair.
• Let \( B \) be the event of picking a black pair.

Since we want to find \( P(\text{brown | black}) \), we can observe that if we have already picked a black pair, we are left with \( 99 \) total pairs (because one pair has already been selected). However, there are still 26 brown pairs remaining.

Thus, the relevant probabilities are:

• \( P(B) \), or the probability of picking a black pair from the total, which is \( \frac{47}{100} \).

While computing \( P(A | B) \):

• The count of brown shoes remains unchanged; we still have \( 26 \) brown pairs regardless of whether a black pair has been selected.

Thus:

\[ P(\text{brown | black}) = \frac{P(\text{brown})}{P(\text{black})} = \frac{26}{99} \]

However, since this scenario doesn't represent choosing a second shoe after the first, the better way to express this situation is the direct proportion of brown shoes remaining if you've picked a black one as a prior choice, which is simply taking into account that:

\[ P(\text{brown | black}) = \frac{26}{99} \]

Thus, \( P(\text{brown | black}) \) is not one of the given response choices but aligns with the understanding of the nature of conditional probabilities.

To find the probabilities based on the provided choices:

1. \( P(B) = \frac{47}{100} \)
2. And assume \( P(A \cap B) \) needs to be understood in terms of the original proportion.

However, from the choices presented, without further refining the problem, it appears that none directly answer \( P(b | b) \) fully with just the context; nonetheless, you would take the conditional provided all counts were separated prior.

Thus, if choosing the closest answer in context to pairs, you would summarize as probable inputs, but again reiterate that \( P(\text{brown | black}) = \text{undefined in standard context without exclusion} \) relating to the selections forward.