Question

There are black, blue, and white marbles in a bag. The probability of choosing a black marble is 0.36. The probability of choosing a black and then a white marble is 0.27. To the nearest hundredth, what is the probability of the second marble being white if the first marble chosen is black?

a) 0.27
b) 0.39
c) 0.75
d) 0.86

Answer 1

Answer: c) 0.75

Step-by-step explanation:

Given : The probability of choosing a black marble is P(Black)= 0.36.

The probability of choosing a black and then a white marble is P( Black and white) = 0.27.

Then by conditional probability ,

The probability of the second marble being white if the first marble chosen is black = $P(\text{white }|\text{Black})=\dfrac{\text{P( Black and white)}}{\text{P(Black}}$

$=\dfrac{0.27}{0.36}=\dfrac{27}{36}=0.75$

Therefore , the probability of the second marble being white if the first marble chosen is black = 0.75