Question 579337: This is my third question asking the same question... I Can't Find it Elsewhere on search boxes Y _ Y
Can someone answer this immediately...
Box A contains 3 white and 4 black balls while Box B contains 4 white and 3 black balls. A ball is taken from Box A and without looking at the color, it is transferred to Box B, then
a.) what is the probability of getting a black ball from Box B,
b.) a white ball from Box B,
c.) if you are to place your bet on the color of the ball that will be taken from box B, in what color are you going to place your bet?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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