SOLUTION: Five counters are selected at random from an urn which contains ten white
and forty black counters. Find the probability that exactly two of the se-
lected counters are white if
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and forty black counters. Find the probability that exactly two of the se-
lected counters are white if
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Question 214953: Five counters are selected at random from an urn which contains ten white
and forty black counters. Find the probability that exactly two of the se-
lected counters are white if the selections are made: (i) without replace-
ment; (ii) with replacement.
In case (i) fnd the probability that at least two of the selected counters
are white. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Five counte/rs are selected at random from an urn which contains ten white
and forty black counters.
Find the probability that exactly two of the selected counters are white
if the selections are made:
(i) without replacement
P(2 white without replacement) = (10/50)(9/49)(40/48)(39/47)(38/46)
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(ii) with replacement
P(2 white with replacement) = 5C2*(10/50)^2(40/50)^3 = 0.2048..
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In case (i) fnd the probability that at least two of the selected counters
are white.
P(at least two white without replacement)
= 1 - [P(none white) + P(1 white)]
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P(none white) = 40C5/50C5
P(one white) = (10/50)(40/49)(39/48)(38/47)(37/46)
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I'll leave the arithmetic to you.
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Cheers,
Stan H.
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