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# Box 1 contains 3 red and 5 white balls, while box 2 contains 4 red and

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Math Expert
Joined: 02 Sep 2009
Posts: 53004
Box 1 contains 3 red and 5 white balls, while box 2 contains 4 red and  [#permalink]

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29 Jan 2019, 02:02
00:00

Difficulty:

35% (medium)

Question Stats:

64% (02:14) correct 36% (01:47) wrong based on 22 sessions

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Box 1 contains 3 red and 5 white balls, while box 2 contains 4 red and 2 white balls. A ball is chosen at random from the first box and placed in the second box without observing its color. Then the ball is drawn from the second box. Find the probability that it is white.

A. 2/7
B. 3/8
C. 3/7
D. 4/7
E. 5/8

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Box 1 contains 3 red and 5 white balls, while box 2 contains 4 red and  [#permalink]

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29 Jan 2019, 02:58
1
Bunuel wrote:
Box 1 contains 3 red and 5 white balls, while box 2 contains 4 red and 2 white balls. A ball is chosen at random from the first box and placed in the second box without observing its color. Then the ball is drawn from the second box. Find the probability that it is white.

A. 2/7
B. 3/8
C. 3/7
D. 4/7
E. 5/8

Probability of Last ball chosen white = Total White balls in Box 2 / Total balls in Box 2

Box 1: 3 red and 5 white balls
Box 2: 4 red and 2 white balls

Case 1: Ball chosen Box 1 is White and then Ball chosen from Box 2 is White
Favourable Probability = Probability of chosen ball white in box 1 * Probability of chosen ball white from box 2

i.e. Favourable Probability = (5/8)*(3/7)

Case 2: Ball chosen Box 1 is Red and then Ball chosen from Box 2 is White
Favourable Probability = Probability of chosen ball Red in box 1 * Probability of chosen ball white from box 2

i.e. Favourable Probability = (3/8)*(2/7)

Total Favourable Probability = Probability of case 1+ Probability of Case 2

i.e. Required Probability = (5/8)*(3/7) + (3/8)*(2/7) = (15+6)/56 = 21/56 = 3/8

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Re: Box 1 contains 3 red and 5 white balls, while box 2 contains 4 red and  [#permalink]

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29 Jan 2019, 03:09
Bunuel wrote:
Box 1 contains 3 red and 5 white balls, while box 2 contains 4 red and 2 white balls. A ball is chosen at random from the first box and placed in the second box without observing its color. Then the ball is drawn from the second box. Find the probability that it is white.

A. 2/7
B. 3/8
C. 3/7
D. 4/7
E. 5/8

we can solve it considering two cases

case 1 : only white balls are chosen from box 1 and is transferred to box 2
P ( white ) ;5/8 * 3/7

case 2: red ball is chosen from box 1 and is transferred to box 2
P (white ) ; 3/8 * 2/7
5/8 * 3/7 + 3/8 * 2/7

15+6/56 = 21/56 ; 3/8
IMO B
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Re: Box 1 contains 3 red and 5 white balls, while box 2 contains 4 red and   [#permalink] 29 Jan 2019, 03:09
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