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Did I compute the probability correctly?
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An urn contains three balls. Each of them may with equal probability be white, green or red. A ball is drawn out of the urn and observed to be white. It is then replaced.
a) Find the probability that all balls in the urn are white
b) Find the probability that the next drawing will give a green ball
A)Each white ball can come out with a probability of 0.333 so the probability of getting three white balls would be 0.037.
B)the probability of getting a green ball after a white ball can be reduced to two cases: either getting a green ball from an urn of 2 green balls or from an urn of one green ball and one white ball
Which is equal to 0.111
Is that correct?
probability
asked Jul 23 at 13:05
Roy Rizk
887
add a comment |Â
up vote
1
down vote
favorite
An urn contains three balls. Each of them may with equal probability be white, green or red. A ball is drawn out of the urn and observed to be white. It is then replaced.
a) Find the probability that all balls in the urn are white
b) Find the probability that the next drawing will give a green ball
A)Each white ball can come out with a probability of 0.333 so the probability of getting three white balls would be 0.037.
B)the probability of getting a green ball after a white ball can be reduced to two cases: either getting a green ball from an urn of 2 green balls or from an urn of one green ball and one white ball
Which is equal to 0.111
Is that correct?
probability
asked Jul 23 at 13:05
Roy Rizk
887
1
The probability that all three balls are white would be $1/27$ only if we had no information about the actual colors of the balls. But we already know that at least one ball is white.
– Joel Reyes Noche
Jul 23 at 13:11
The answer I posted earlier was WRONG. I computed the probability that there are $3$ white balls, given that there is at least one ball, but we actually know more than that. The fact that the first ball was white makes it more like that we had two whites and a red than two reds and a white, say.
– saulspatz
Jul 23 at 15:33
Can you explain to me the part b of the solution?
– Roy Rizk
Jul 23 at 18:25
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
An urn contains three balls. Each of them may with equal probability be white, green or red. A ball is drawn out of the urn and observed to be white. It is then replaced.
a) Find the probability that all balls in the urn are white
b) Find the probability that the next drawing will give a green ball
A)Each white ball can come out with a probability of 0.333 so the probability of getting three white balls would be 0.037.
B)the probability of getting a green ball after a white ball can be reduced to two cases: either getting a green ball from an urn of 2 green balls or from an urn of one green ball and one white ball
Which is equal to 0.111
Is that correct?
probability
asked Jul 23 at 13:05
Roy Rizk
887
An urn contains three balls. Each of them may with equal probability be white, green or red. A ball is drawn out of the urn and observed to be white. It is then replaced.
a) Find the probability that all balls in the urn are white
b) Find the probability that the next drawing will give a green ball
A)Each white ball can come out with a probability of 0.333 so the probability of getting three white balls would be 0.037.
B)the probability of getting a green ball after a white ball can be reduced to two cases: either getting a green ball from an urn of 2 green balls or from an urn of one green ball and one white ball
Which is equal to 0.111
Is that correct?
probability
asked Jul 23 at 13:05
Roy Rizk
887
asked Jul 23 at 13:05
Roy Rizk
887
asked Jul 23 at 13:05
Roy Rizk
887
asked Jul 23 at 13:05
Roy Rizk
887
887
1
The probability that all three balls are white would be $1/27$ only if we had no information about the actual colors of the balls. But we already know that at least one ball is white.
– Joel Reyes Noche
Jul 23 at 13:11
The answer I posted earlier was WRONG. I computed the probability that there are $3$ white balls, given that there is at least one ball, but we actually know more than that. The fact that the first ball was white makes it more like that we had two whites and a red than two reds and a white, say.
– saulspatz
Jul 23 at 15:33
Can you explain to me the part b of the solution?
– Roy Rizk
Jul 23 at 18:25
add a comment |Â
1
The probability that all three balls are white would be $1/27$ only if we had no information about the actual colors of the balls. But we already know that at least one ball is white.
– Joel Reyes Noche
Jul 23 at 13:11
The answer I posted earlier was WRONG. I computed the probability that there are $3$ white balls, given that there is at least one ball, but we actually know more than that. The fact that the first ball was white makes it more like that we had two whites and a red than two reds and a white, say.
– saulspatz
Jul 23 at 15:33
Can you explain to me the part b of the solution?
– Roy Rizk
Jul 23 at 18:25
1
1
The probability that all three balls are white would be $1/27$ only if we had no information about the actual colors of the balls. But we already know that at least one ball is white.
– Joel Reyes Noche
Jul 23 at 13:11
The probability that all three balls are white would be $1/27$ only if we had no information about the actual colors of the balls. But we already know that at least one ball is white.
– Joel Reyes Noche
Jul 23 at 13:11
The answer I posted earlier was WRONG. I computed the probability that there are $3$ white balls, given that there is at least one ball, but we actually know more than that. The fact that the first ball was white makes it more like that we had two whites and a red than two reds and a white, say.
– saulspatz
Jul 23 at 15:33
The answer I posted earlier was WRONG. I computed the probability that there are $3$ white balls, given that there is at least one ball, but we actually know more than that. The fact that the first ball was white makes it more like that we had two whites and a red than two reds and a white, say.
– saulspatz
Jul 23 at 15:33
Can you explain to me the part b of the solution?
– Roy Rizk
Jul 23 at 18:25
Can you explain to me the part b of the solution?
– Roy Rizk
Jul 23 at 18:25
add a comment |Â
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1
The probability that all three balls are white would be $1/27$ only if we had no information about the actual colors of the balls. But we already know that at least one ball is white.
– Joel Reyes Noche
Jul 23 at 13:11
The answer I posted earlier was WRONG. I computed the probability that there are $3$ white balls, given that there is at least one ball, but we actually know more than that. The fact that the first ball was white makes it more like that we had two whites and a red than two reds and a white, say.
– saulspatz
Jul 23 at 15:33
Can you explain to me the part b of the solution?
– Roy Rizk
Jul 23 at 18:25