probability theory

Question

a box contains 5 white and 7 black balls, two sucessive drawn of 3 balls are made 1. with replacement 2. without replacement .  the probability that the first draw would produce white balls  and the second draw would produce black balls re respecively

Answer 1

The probability of selecting a white ball is 5/12 and a black ball 7/12.

(1) The probability of selecting another white ball when the first is replaced is (5/12)², and then, after replacing the second ball, selecting a third white ball is (5/12)³=125/1728 (7.23% approx).

For three black balls similarly selected and replaced the probability is 343/1728 (19.85% approx).

(2) If the balls are not replaced, the white ball selection probability is (5/12)(4/11)(3/10)=1/22 (4.56% approx).

Similarly, for the black balls the probability is (7/12)(6/11)(5/10)=7/44 (15.91% approx).