A bag contains 4 red balls and 5 blue balls. Two balls are drawn randomly without replacement. Given that the first ball...

Question

A bag contains 4 red balls and 5 blue balls. Two balls are drawn randomly without replacement. Given that the first ball drawn is red, the probability (rounded off to 3 decimal places) that both balls drawn are red is ___________.

Accepted Answer

0.375 We want the conditional probability that the second ball is also red, given the first ball drawn was red. Since drawing is without replacement, after removing one red ball the composition of the bag changes. We use the definition P(A|B) = P(A and B) / P(B), but the simpler direct method is to note that after one red ball is removed, the updated bag has 3 red and 5 blue balls (8 total).