young_gun wrote:

There are 18 shirts in a closet. 12 are stripes and 6 are white. 6 draws are made of 1 shirt at a time without any replacement of which at least 4 are found to be white. What is the probability that in the next 2 draws, exactly 1 shirt is white?

My take

2 things to note:

A. without any replacement

B.at least 4 are found to be white

A =>

6 shirts are already out so total number of shirts is 12 for next 2 draws.

B =>

we have 3 cases

Case 1)4 white shirts and 2 striped shirts taken out => 2 white & 10 striped remain

Case 2)5 white shirts and 1 striped shirt taken out => 1 white and 11 striped remain

Case 3)6 white shirts and 0 striped shirt takes out => 0 white and 12 striped remain

What we want is

>the probability that in the next 2 draws, exactly 1 shirt is white?

for case 1

P(W|S) = ( 2/12 * 10/11) / 10/11 OR

P(S|W) = (10/12 * 2/11)/ 2/11

P(case 1) = 1 (????)

for case 2

P(W|S) = ( 1/12 * 11/11) / 11/11 OR

P(S|W) = (11/12 * 1/11)/ 1/11

so case 3) is ignored as no white shirts present. = 0

&.... I have screwed somewhere!