An urn contains one white chip and a second chip that is equally likely to be white or black. A chip is drawn at random and returned to the urn. Then a second chip is drawn. What is the probability that a white appears on the second draw given that a white appeared on the first draw? (Hint: Let W i be the event that a white chip is selected on the i th draw, i = 1 , 2 . Then P ( W 2 | W 1 ) = P ( W 1 ∩ W 2 ) P ( W 1 ) . If both chips in the urn are white, P ( W 1 ) = 1 ; otherwise, P ( W 1 ) = 1 2 .)
An urn contains one white chip and a second chip that is equally likely to be white or black. A chip is drawn at random and returned to the urn. Then a second chip is drawn. What is the probability that a white appears on the second draw given that a white appeared on the first draw? (Hint: Let W i be the event that a white chip is selected on the i th draw, i = 1 , 2 . Then P ( W 2 | W 1 ) = P ( W 1 ∩ W 2 ) P ( W 1 ) . If both chips in the urn are white, P ( W 1 ) = 1 ; otherwise, P ( W 1 ) = 1 2 .)
Solution Summary: The author explains that the probability that a white appears on the second draw is 5/6.
An urn contains one white chip and a second chip that is equally likely to be white or black. A chip is drawn at random and returned to the urn. Then a second chip is drawn. What is the probability that a white appears on the second draw given that a white appeared on the first draw? (Hint: Let
W
i
be the event that a white chip is selected on the ith draw,
i
=
1
,
2
. Then
P
(
W
2
|
W
1
)
=
P
(
W
1
∩
W
2
)
P
(
W
1
)
. If both chips in the urn are white,
P
(
W
1
)
=
1
; otherwise,
P
(
W
1
)
=
1
2
.)
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