- #1
naspek
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box A contains 2 red balls,
box B contains 2 white balls,
box C contains 1 red ball and 1 white ball,
A box is selected at random (with equal probabilities) and one ball is taken at random from that box.
(i) Compute the probability of selecting a white ball using Bayes Rule.
A(1/3) _____ Red(1/6)
...|____ Red(1/6)
B(1/3)______White(1/6)
...|_____White(1/6)
C(1/3)______Red(1/6)
...|_____White(1/6)
so.. P(White) = [(1/3)*(1/6)] + [(1/3)*(1/6)] + [(1/3)*(1/6)]
= 1/6
Correct?
(ii)Compute the conditional probability that B has been selected given that the ball is white.
P(B|White) = P(B intersect White) / P(White)
what is my P(B intersect White)?
box B contains 2 white balls,
box C contains 1 red ball and 1 white ball,
A box is selected at random (with equal probabilities) and one ball is taken at random from that box.
(i) Compute the probability of selecting a white ball using Bayes Rule.
A(1/3) _____ Red(1/6)
...|____ Red(1/6)
B(1/3)______White(1/6)
...|_____White(1/6)
C(1/3)______Red(1/6)
...|_____White(1/6)
so.. P(White) = [(1/3)*(1/6)] + [(1/3)*(1/6)] + [(1/3)*(1/6)]
= 1/6
Correct?
(ii)Compute the conditional probability that B has been selected given that the ball is white.
P(B|White) = P(B intersect White) / P(White)
what is my P(B intersect White)?