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There are 3 boxes labeled A, B and C. Box A contains 6 coins, 1 of which is made of gold

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There are 3 boxes labeled A, B and C. Box A contains 6 coins, 1 of which is made of gold

by Brent@GMATPrepNow » Sun Aug 28, 2022 12:25 pm

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There are 3 boxes labeled A, B and C. Box A contains 6 coins, 1 of which is made of gold. Box B contains 4 coins, 1 of which is made of gold. Box C contains 2 coins, 1 of which is made of gold. If a box is randomly selected, and a coin is randomly selected from that box, what is the probability the selected coin is made of gold?

A) 1/12
B) 1/4
C) 11/36
D) 1/3
E) 5/12

Answer: C
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GMAT/MBA Expert

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Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
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Re: There are 3 boxes labeled A, B and C. Box A contains 6 coins, 1 of which is made of gold

by Brent@GMATPrepNow » Mon Aug 29, 2022 6:38 am
Brent@GMATPrepNow wrote: ↑
Sun Aug 28, 2022 12:25 pm
 There are 3 boxes labeled A, B and C. Box A contains 6 coins, 1 of which is made of gold. Box B contains 4 coins, 1 of which is made of gold. Box C contains 2 coins, 1 of which is made of gold. If a box is randomly selected, and a coin is randomly selected from that box, what is the probability the selected coin is made of gold?

A) 1/12
B) 1/4
C) 11/36
D) 1/3
E) 5/12

Answer: C
Source: www.gmatprepnow.com
P(selected coin is made of gold) = P(select box A AND select gold coin from box A OR select box B AND select gold coin from box B OR P(select box C AND select gold coin from box C)

= [P(select box A) x P(select gold coin from box A)] + [P(select box B) x P(select gold coin from box B)] + [P(select box C) x P(select gold coin from box C)]

= [1/3 x 1/6] + [1/3 x 1/4] + [1/3 x 1/2]

= 1/3(1/6 + 1/4 + 1/2)

= 11/36

Answer: C
Brent Hanneson - Creator of GMATPrepNow.com
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