Question 906010: box 1 contains 4 yellow balls and 2 green balls. box 2 contains 5 green balls and 3 yellow balls. a coin is tossed. if it lands heads up, box 1 is selected and a ball is drawn. if it lands tails up, box 2 is selected and a ball is drawn. find the probability of selecting a yellow ball
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! box 1 contains 4 yellow and 2 green.
box 2 contains 5 green and 3 yellow
the probability of getting a yellow out of box 1 is 4/6 = 1/3.
the probability of getting a yellow out of box 2 is 3/8.
when you toss a coin, the probably of it coming up heads is 1/2 and the probability of it coming up tails is 1/2.
the probability of flipping a head and getting a yellow ball is therefore 1/2 * 1/3 = 1/6.
the probability of flipping a tail and getting a yellow ball is therefore 1/2 * 3/8 = 3/16.
since flipping a head or a tail are totally independent events, then the probability of flipping a head or a tail is equal to 1/2 + 1/2 = 1.
the probability of getting a yellow is therefore the probability of flipping a head and getting a yellow or flipping a tail and getting a yellow.
those probabilities are 1/6 for the head and 3/16 for the tail.
the overall probability is therefore 1/6 + 3/16 = = 8/48 + 9/48 = 17/48.
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