Question

A bag contains blue and yellow marbles. Two marbles are drawn without replacement. The probability of selecting a blue marble and then a yellow marble is 0.37, and the probability of selecting a blue marble on the first draw is 0.55.
What is the probability of selecting a yellow marble on the second draw, if the first marble drawn was blue?
A) 18%
B) 20%
C) 46%
D) 67%

Answer 1

Let b = blue marbles
y = yellow marbles
 Sum = b+y
 The chance of a blue marble being drawn first is:
b / (b+y) = 0.55 
The chance of a blue marble being drawn first then a yellow next is:
b / (b+y) * y / (b+y-1) = 0.37
This can be solve easily by using a theorem of Bayes 
0.37/0.55 = .67 or 67%