What is the probability of neither being red given that neither is blue?

Question

For this problem, assume the box contains 3 red balls, 5 blue balls, and 8 white balls, and that we choose two balls at random from the box.
What is the probability of neither being red given that neither is blue?

Answer 1

It was given that tow balls were drawn out of 16 (3red, 5 blue, 8 white).

 

It is further given that neither of the two balls were blue.  That fact means that the two balls were both red, one red and one white, or both white.

 

But, in the question, we were asked about the "probability of neither being red ". That fact means that both of the balls were white.

 

So, the question is "What is the chance that the two balls are both white?"

When the first ball was drawn, the chance was 8 white balls out of 16 balls, or 50%%

 

When the second ball was drawn, there were 7 white balls out of 15 balls, or 46.6%

 

The probability of the two events is the product of the individual events, or 0.5 x 0.466 = 0.233 = 23.3%