Question 579337
bet on the white ball.
here's why i think that way.


box a contains 3 white and 4 black
box b contains 4 white and 3 black.


if a white ball is transferred from box a to box b, then:
box b contains 5 white and 3 black.


if a black ball is transferred from box a to box b, then:
box b contains 4 white and 4 black.


a white ball is transferred from box a to box b 3/7 of the time because the probability of extracting a white ball from box a is 3/7.


a black ball is transferred from box a to box b 4/7 of the time because the probability of extracting a black ball from box b is 4/7.


this means that 3/7 of the time box b will contain 5 white balls and 3 black balls and 4/7 of the time box b will contain 4 white balls and 4 black balls.


this means that 3/7 of the time, the probability of getting a white ball from box b is 5/8 and 4/7 of the time the probability of getting a white ball from box b is 4/8.


this also means that 3/7 of the time, the probability of getting a black ball from box b is 3/8 and 4/7 of the time, the probability of getting a black ball from box b is 4/8.


the combined probability of getting a white ball out of box b is 3/7 * 5/8 + 4/7 * 4/8 which is equal to 15/56 + 16/56 which is equal to 31/56.


the combined probability of getting a black ball out of box b is 3/7 * 3/8 + 4/7 * 4/8 which is equal to 9/56 + 16/56 which is equal to 25/56


the probability of getting a white ball is higher than the probability of getting a black ball from box b.


this is why you should bet on white.


the total probability is the combined probability of getting a white ball plus the combined probability of getting a black ball which is 25/56 plus 31/56 = 56/56 which is equal to 1 which is as it should be.


the odds of getting a white ball is equal to the probability of getting a white ball divided by the probability of getting a black ball which is equal to 31/25.