# Conditional Event

• Feb 6th 2010, 06:22 PM
cyt91
Conditional Event
A box contains 5 green marbles and 4 yellow marbles. Three marbles are drawn at random from the box without replacement. Find the probability that at least 2 yellow marbles are drawn given that at least one of each colour is drawn.

I've calculated the probability of drawing at least one of each colour is drawn. It's 5/6. The probability of drawing at least 2 yellow marbles is 17/42.

Now, how do I calculate the probability that at least 2 yellow marbles are drawn given that at least one of each colour is drawn? Many thanks in advance! (Bow)
• Feb 6th 2010, 07:13 PM
Quote:

Originally Posted by cyt91
A box contains 5 green marbles and 4 yellow marbles. Three marbles are drawn at random from the box without replacement. Find the probability that at least 2 yellow marbles are drawn given that at least one of each colour is drawn.

I've calculated the probability of drawing at least one of each colour is drawn. It's 5/6. The probability of drawing at least 2 yellow marbles is 17/42.

Now, how do I calculate the probability that at least 2 yellow marbles are drawn given that at least one of each colour is drawn? Many thanks in advance! (Bow)

hi

do you recognise this ? P(A|B)=P(A n B)/P(B)

so the condition here is at least one of each colour is drawn , call it B

and the event that at least 2 yellow marbles are drawn , A

P(A n B)=(5C1 x 4C2)/9C3=5/14

so P(A|B)=(5/14)/(5/6)=3/7
• Feb 6th 2010, 07:41 PM
cyt91
Thanks. Found it.(Wink)