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 plus Start Fraction 47 over 99 End Fraction
26100
Start Fraction 26 over 100 End Fraction
26100⋅47100
Start Fraction 26 over 100 End Fraction times Start Fraction 47 over 100 End Fraction
26100⋅4799
?(1 point)
Responses
26100+4799
Start Fraction 26 over 100 End Fraction plus Start Fraction 47 over 99 End Fraction
26100
Start Fraction 26 over 100 End Fraction
26100⋅47100
Start Fraction 26 over 100 End Fraction times Start Fraction 47 over 100 End Fraction
26100⋅4799
Answers
GPT-4o mini
To find \( P(\text{brown} | \text{black}) \), which is the probability of selecting a brown pair given that a black pair has been selected, we can use the formula for conditional probability:
\[
P(A | B) = \frac{P(A \cap B)}{P(B)}
\]
Where:
- \( A \) is the event of selecting a brown pair.
- \( B \) is the event of selecting a black pair.
However, since brown and black are mutually exclusive categories of shoe pairs (you can't select a pair that is both brown and black at the same time), the probability of selecting a brown pair given that a black pair has been selected is 0.
Therefore, \( P(\text{brown} | \text{black}) = 0 \).
None of the options provided correspond to this conclusion. If you meant a different probability, please clarify.
\[
P(A | B) = \frac{P(A \cap B)}{P(B)}
\]
Where:
- \( A \) is the event of selecting a brown pair.
- \( B \) is the event of selecting a black pair.
However, since brown and black are mutually exclusive categories of shoe pairs (you can't select a pair that is both brown and black at the same time), the probability of selecting a brown pair given that a black pair has been selected is 0.
Therefore, \( P(\text{brown} | \text{black}) = 0 \).
None of the options provided correspond to this conclusion. If you meant a different probability, please clarify.