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A bag contains 3 red balls and 2 blue balls a ball is taken at random from the bag and then put back what is the probability that both balls are red?
Wiki User
∙ 12y ago
3c2+2c2+3c1 2c1
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7c2.
I have done it this way. 3C2 means that the both balls would be green 2C2 both would be red and 3C1 and 2C1 because both the balls can be red and green.
Wiki User
∙ 12y ago
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the odds theoretically are almost infinity to 1 as they could be any color. -------------------------------------------------------------------------------------------2nd opinionLet's say we have 3 boxes with 4 balls each.Box A has 4 white balls.Box B has 3 white balls.Box C has 2 white balls.The probability of drawing 2 W balls from;Box A, P(2W│A)=(4/4)∙(3/3)=1Box B, P(2W│B)=(3/4)∙(2/3)=1/2Box C, P(2W│C)=(2/4)∙(1/3)=1/6Say the probability of picking any of the 3 boxes is the same, we have;P(A)=1/3P(B)=1/3P(C)=1/3Question is, given the event of drawing 2 W balls from a box taken blindlyfrom the 3 choices, what is the probability that the balls came from box A,P(A│2W).Recurring to Bayes Theorem:P(A│2W)=[P(A)P(2W│A)]/[P(A)P(2W│A)+P(B)P(2W│B)+P(C)P(2W│C)]=[(1/3)(1)]/[(1/3)(1)+(1/3)(1/2)+(1/3)(1/6)]=6/10=0.60=60%P(A│2W)=0.60=60%Read more:Solution_to_a_bag_contains_4_balls_Two_balls_are_drawn_at_random_and_are_found_to_be_white_What_is_the_probability_that_all_balls_are_white
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Solution to a bag contains 4 balls Two balls are drawn at random and are found to be white What is the probability that all balls are white?
Two balls are certainly white. So the remaining balls may be one of the following{WW, WN, NW, NN}where W means a white ball and N means non-whiteballLet the events be:E- all four balls are white(WW)F- 3 balls are white(WN,NW)G- only two balls are white(NN)Now, P(E) =P(G) =1/4, and P(F) =1/2Let A be the event that the two balls drawn are whiteP(A|E)=4C2/4C2 =1P(A|F)=3C2/4C2 =1/2P(A|G)=2C2/4C2 =1/6Now By Bayes' Theorem,required probability =P(E|A)=(1*1/4) / ( 1*1/4 + 1/2*1/2 + 1/6*1/4 )=(1/4) / ( 13/24 )=6/13----------------------------------------------------------------------------------------------------2nd opinionLet's say we have 3 boxes with 4 balls each.Box A has 4 white balls.Box B has 3 white balls.Box C has 2 white balls.The probability of drawing 2 W balls from;Box A, P(2W│A) =(4/4)∙(3/3) =1Box B, P(2W│B) =(3/4)∙(2/3) =1/2Box C, P(2W│C) =(2/4)∙(1/3) =1/6Say the probability of picking any of the 3 boxes is the same, we have;P(A) =1/3P(B) =1/3P(C) =1/3Question is, given the event of drawing 2 W balls from a box taken blindlyfrom the 3 choices, what is the probability that the balls came from box A,P(A│2W).Recurring to Bayes Theorem:P(A│2W) =[P(A)P(2W│A)]/[P(A)P(2W│A)+P(B)P(2W│B)+P(C)P(2W│C)] =[(1/3)(1)]/[(1/3)(1)+(1/3)(1/2)+(1/3)(1/6)] =6/10 =0.60 =60%P(A│2W) =0.60 =60%
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The answer depends on where in the world the random selection is taken since the location will determine the mix of cars that the selection is made from.
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97% chance of selecting a good one
A bag A conatins 5 dimes and 2 quarters and bag B contains 1 dime and 3 quartersIf a coin is taken from one of the two bags at random what is the probability that the coin is a quarter?
Now the 2 bags contain a total of 6 dimes and 5 quarters, which is a total of 11 coins. Therefore, the probability of getting a quarter is (5/11) which is about 0.4545.... or 45.45% as the case may be. Hope this helps
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A bag contains 4balls two balls are drawn at random and are found to be white what is the probability that all balls are white?
the odds theoretically are almost infinity to 1 as they could be any color. -------------------------------------------------------------------------------------------2nd opinionLet's say we have 3 boxes with 4 balls each.Box A has 4 white balls.Box B has 3 white balls.Box C has 2 white balls.The probability of drawing 2 W balls from;Box A, P(2W│A)=(4/4)∙(3/3)=1Box B, P(2W│B)=(3/4)∙(2/3)=1/2Box C, P(2W│C)=(2/4)∙(1/3)=1/6Say the probability of picking any of the 3 boxes is the same, we have;P(A)=1/3P(B)=1/3P(C)=1/3Question is, given the event of drawing 2 W balls from a box taken blindlyfrom the 3 choices, what is the probability that the balls came from box A,P(A│2W).Recurring to Bayes Theorem:P(A│2W)=[P(A)P(2W│A)]/[P(A)P(2W│A)+P(B)P(2W│B)+P(C)P(2W│C)]=[(1/3)(1)]/[(1/3)(1)+(1/3)(1/2)+(1/3)(1/6)]=6/10=0.60=60%P(A│2W)=0.60=60%Read more:Solution_to_a_bag_contains_4_balls_Two_balls_are_drawn_at_random_and_are_found_to_be_white_What_is_the_probability_that_all_balls_are_white
