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⋅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 26100 Start Fraction 26 over 100 End Fraction
Answers
GPT-4o mini
To find \( P(\text{brown} | \text{black}) \), we need to use the formula for conditional probability:
\[
P(A | B) = \frac{P(A \cap B)}{P(B)}
\]
In this case:
- \( A \) is the event of having a brown pair of shoes.
- \( B \) is the event of having a black pair of shoes.
Since brown and black are two distinct categories of shoes, the events \( A \) and \( B \) cannot occur simultaneously. Therefore, \( P(A \cap B) = 0 \).
This implies:
\[
P(\text{brown} | \text{black}) = \frac{P(\text{brown} \cap \text{black})}{P(\text{black})} = \frac{0}{P(\text{black})} = 0
\]
Thus, the answer to \( P(\text{brown} | \text{black}) \) is \( 0 \).
None of the provided options directly match this reasoning, indicating an inherent misunderstanding of the problem concept, so the correct conclusion based on the probability context is:
\[
P(brown | black) = 0
\]
If you are looking for specific numerical answers from the options listed, please clarify, and I can reassess based on further details!
\[
P(A | B) = \frac{P(A \cap B)}{P(B)}
\]
In this case:
- \( A \) is the event of having a brown pair of shoes.
- \( B \) is the event of having a black pair of shoes.
Since brown and black are two distinct categories of shoes, the events \( A \) and \( B \) cannot occur simultaneously. Therefore, \( P(A \cap B) = 0 \).
This implies:
\[
P(\text{brown} | \text{black}) = \frac{P(\text{brown} \cap \text{black})}{P(\text{black})} = \frac{0}{P(\text{black})} = 0
\]
Thus, the answer to \( P(\text{brown} | \text{black}) \) is \( 0 \).
None of the provided options directly match this reasoning, indicating an inherent misunderstanding of the problem concept, so the correct conclusion based on the probability context is:
\[
P(brown | black) = 0
\]
If you are looking for specific numerical answers from the options listed, please clarify, and I can reassess based on further details!