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Box A contains 2 black chips. Box B contains 2 white chips.

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Box A contains 2 black chips. Box B contains 2 white chips.

by Brent@GMATPrepNow » Thu May 14, 2020 7:03 am

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Box A contains 2 black chips. Box B contains 2 white chips. Box C contains 1 black chip and 1 white chip. Ted chooses a box at random and then randomly selects a chip from that box. If the selected chip is black, what is the probability that the other chip in the same box is also black?

A) 1/5
B) 1/4
C) 1/3
D) 1/2
E) 2/3

Answer: E
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GMAT/MBA Expert

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Re: Box A contains 2 black chips. Box B contains 2 white chips.

by Brent@GMATPrepNow » Fri May 15, 2020 8:54 am
Brent@GMATPrepNow wrote: ↑
Thu May 14, 2020 7:03 am
 Box A contains 2 black chips. Box B contains 2 white chips. Box C contains 1 black chip and 1 white chip. Ted chooses a box at random and then randomly selects a chip from that box. If the selected chip is black, what is the probability that the other chip in the same box is also black?

A) 1/5
B) 1/4
C) 1/3
D) 1/2
E) 2/3

Answer: E
Source: www.gmatprepnow.com
Let’s let:
B1 be one black chip in Box A.
B2 be the other black chip in Box A.
W1 be one white chip in Box B.
W2 be the other white chip in Box B.
B3 be the black chip in Box C
W3 be the white chip in Box C

There are 6 EQUALLY LIKELY outcomes:
Case i: Ted selects B1 from box A
Case ii: Ted selects B2 from box A
Case iii: Ted selects W1 from box B
Case iv: Ted selects W2 from box B
Case v: Ted selects B3 from box C
Case vi: Ted selects W3 from box C

If the selected chip is black, then we’re dealing with cases i, ii, or v
All 3 cases are EQUALLY LIKELY
In case i, the other chip is also black
In case ii, the other chip is also black
In case v, the other chip is white

So, of the 3 possible cases, 2 cases are such that the other chip in the box is black.

P(other chip is black) = 2/3

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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