crackgmat007 wrote:A basket contains 3 white and 5 blue balls. Mary will extract one ball at random and keep it. If, after that, John will extract one ball at random, what is the probability that John will extract a blue ball?

This question reminds me of my childhood, when my friends and I would sometimes "draw straws" to randomly select one person to do something (often either work, like getting wood for the fire, or dumb, like eating something that shouldn't be eaten).

So, someone would hold up n pieces of grass (for n guys), and one of those pieces was very short. The person who selected the shortest piece was the one who had to perform the task.

There was always one guy who wanted to choose his piece last. His reasoning was that his chances of drawing the shortest piece were minimized since every person before him had a chance of drawing the short piece before it got to his turn.

The truth of the matter is that each of the n guys had a 1/n chance of selecting the shortest piece, regardless of the order in which they selected.

The same applies to the original question here. 5 of the 8 balls are blue, so P(John selects a blue ball) = 5/8

Cheers,
Brent

crackgmat007 wrote:A basket contains 3 white and 5 blue balls. Mary will extract one ball at random and keep it. If, after that, John will extract one ball at random, what is the probability that John will extract a blue ball?

Let's solve this question a different way.

P(John gets blue ball) = P(Mary gets white ball and John gets blue ball OR Mary gets blue ball and John gets blue ball
= P(Mary gets white ball and John gets blue ball) + P(Mary gets blue ball and John gets blue ball)
= (3/8 x 5/7) + (5/8 x 4/7)
= 15/56 + 20/56
= 35/56
= 5/8

Answer: still D

Cheers,
Brent