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)
𝑃
(
brown
|
black
)
?(1 point)
Responses

26100⋅47100
26
100
⋅
47
100

Start Fraction 26 over 100 End Fraction times Start Fraction 47 over 100 End Fraction

26100⋅4799
26
100
⋅
47
99

Start Fraction 26 over 100 End Fraction times Start Fraction 47 over 99 End Fraction

26100+4799
26
100
+
47
99

Start Fraction 26 over 100 End Fraction plus Start Fraction 47 over 99 End Fraction

47100⋅2699
47
100
⋅
26
99

Start Fraction 47 over 100 End Fraction times start Fraction 26 over 99

Answer 1

P(brown | black) = 26/99.

Reason: if one pair is known to be black, there are 99 pairs left and 26 of them are brown, so the conditional probability is 26/99. (Note: 47/100·26/99 is the joint probability of drawing a black then a brown.)