Question 1135130: Rework problem 28 from section 3.4 of your text, involving the drawing of two balls from a box of colored balls. Assume the box contains 10 balls: 5 red, 3 blue, and 2 yellow. A ball is drawn and its color noted. If the ball is yellow, it is replaced; otherwise, it is not. A second ball is then drawn and its color is noted.
What is the probability that the first ball was yellow, given that the second was red?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! One can make a tree diagram and determine that
RR is 2/9
RB is 1.5/9
RY is 1/9
BR is 1.5/9
BB is .6/9
BY is .6/9
YR is 1/10
YB is 6/100
YY is 4/100
Those do add to 1.00
So, if the second is red 10/100+15/90+20/90 or 35/90 + 10/100 or 440/900,
the first one was yellow is 10/100 or 90/900
The answer is 90/440 or 0.2045
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