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A certain prize game has three different types of prizes and one of th

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jfdelgado
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A certain prize game has three different types of prizes and one of th [#permalink] New post   11 Jan 2020, 13:08
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A certain prize game has three different types of prizes and one of them is given at random when a player wins. If a certain player plays and wins 3 times, what is the probability that the player receives one of each type of prize?
A. 0
B. 1/9
C. 2/9
D. 1/3
E. 1
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C
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BrentGMATPrepNow
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Re: A certain prize game has three different types of prizes and one of th [#permalink] New post   14 Jan 2020, 07:05
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jfdelgado wrote:
A certain prize game has three different types of prizes and one of them is given at random when a player wins. If a certain player plays and wins 3 times, what is the probability that the player receives one of each type of prize?
A. 0
B. 1/9
C. 2/9
D. 1/3
E. 1


P(player gets one of each prize) = P(1st prize is ANY prize AND 2nd prize is different from 1st prizes AND 3rd prize is different from prize 1 and 2)
= P(1st prize is ANY prize) x P(2nd prize is different from 1st prize) x P(3rd prize is different from prize 1 and 2)
= 3/3 x 2/3 x 1/3
= 2/9

Answer: C

Cheers,
Brent
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Re: A certain prize game has three different types of prizes and one of th [#permalink] New post   14 Jan 2020, 16:48
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1st time - can win any of the 3 prices- probability = 3/3=1
2nd time - remaining 2 out of 3 prices - prob = 2/3 in the same way
3rd time - probability - 1/3

total= 1*(2/3)*(1/3)=2/9

Ans choice C
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Re: A certain prize game has three different types of prizes and one of th [#permalink] New post   28 Aug 2021, 05:38
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Solution:

According to the question, the player needs to win 3 different prizes in 3 games.

Probability of winning \(1st\) prize in game \(1 = \frac{3}{3} = 1\)

Probability of winning 2nd prize (different from first) in game \(2 = \frac{2}{3} \)

Probability of winning 3rd prize (different from first two) in game \(3 = \frac{1}{3}\)

Thus total probability \(= 1\times \frac{2}{3} \times \frac{1}{3} = \frac{2}{9}\)

Hence the right answer is Option C.
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Re: A certain prize game has three different types of prizes and one of th [#permalink] New post   29 Aug 2021, 09:04
Probability of getting one of each type = 3!/(3.3.3) = 6/27 = 2/9
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Re: A certain prize game has three different types of prizes and one of th [#permalink] New post   10 Dec 2023, 14:26
Hello from the GMAT Club BumpBot!

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Re: A certain prize game has three different types of prizes and one of th [#permalink]
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