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21 Jun 2011, 08:53
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Julia and Brain play a game in which Julia takes a ball and
if it is green, she wins. If the first ball is not green, she takes the second ball (without
replacing
first) and she wins if the two balls are white or if the first ball is gray and the second ball is
white. What is the probablity of winning if the jar contains 1 gray, 2 white, and 4 green balls?
if it is green, she wins. If the first ball is not green, she takes the second ball (without
replacing
first) and she wins if the two balls are white or if the first ball is gray and the second ball is
white. What is the probablity of winning if the jar contains 1 gray, 2 white, and 4 green balls?
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21 Jun 2011, 09:02
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shs0145
here it goes:)
1Gray, 2 white and 4 green .
probability of picking the ball as green = 4/7( or 4c1/7c1).. she wins
suppose she picks the first as gray = 1/7 and next white = 2/6( 6 because not replacing) = 1/7*2/6= 2/42..she wins
suppose she picks white first = 2/7 and then gray = 1/6 .. she wins = 2/7*1/6 = 2/42
total probability is
4/7+2/42+2/42 = 24/42+4/42= 28/42 = 2/3...
hope this helps
21 Jun 2011, 13:19
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There are 3 scenario's to win the game:
1) Pick green right away! Out of the 7 balls, the probability to pick one green in one pick is 4/7
2) Two white balls: 2/7 * 1/6 = 2/42
3) Grey First, White After: 1/7 * 2/6 =2/42
Because all these events can not happen simultaneously, you have to add the probabilities in order to get the total probability of winning the game.
4/7+2/42+2/42 = 2/3
1) Pick green right away! Out of the 7 balls, the probability to pick one green in one pick is 4/7
2) Two white balls: 2/7 * 1/6 = 2/42
3) Grey First, White After: 1/7 * 2/6 =2/42
Because all these events can not happen simultaneously, you have to add the probabilities in order to get the total probability of winning the game.
4/7+2/42+2/42 = 2/3
