Question

3.14. An urn initially contains 5 white and 7 black balls. Each time a ball is selected, its color is noted and it is replaced in the urn along with 2 other balls of (a) the first 2 balls selected are black and the next 2 are white (b) of the first 4 balls selected, exactly 2 are black.

Answer 1

a)let a black and white ball are reperesented by B and W

a)P(first 2 are black and next 2 are Black)=P(BBWW)=(7/12)*(9/14)*(5/16)*(7/18)=2205/45360

b)

P(exactly 2 are black)=P(BBWW)+P(BWBW)+P(BWWB)+P(WBBW)+P(WBWB)+P(WWBB)

=6*(7/12)*(9/14)*(5/16)*(7/18)=13230/45360