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Frank has a box containing 6 doughnuts: 3 jellies and 3

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by AAPL » Mon Jun 25, 2018 12:39 pm

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Answers

A

B

C

D

E

Stats

Difficulty—

Frank has a box containing 6 doughnuts: 3 jellies and 3 cinnamon twists. If Frank eat 3 doughnuts, chosen randomly from the box, what is the probability that he eats 3 jelly doughnuts?

A. 1/2
B. 1/3
C. 1/8
D. 1/20
E. 1/36

The OA is D.

The total possibilities of finding a doughnut is 6c3 or 20.

Similarly, if we need to find if all the doughnuts picked by Frank are jelly doughnuts, the possibility is 3c3 or 1.

The probability of such an event occurring is 1/20.

Has anyone another strategic approach to solve this PS question? Regards!
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by [email protected] » Mon Jun 25, 2018 4:15 pm
Hi All,

We're told that Frank has a box containing 6 doughnuts: 3 jellies and 3 cinnamon twists - and that Frank eats 3 doughnuts (chosen randomly from the box). We're asked for the probability that he eats the 3 jelly doughnuts. This question can be solved as a Combination Formula question or as a Permutation.

Since there are 3 jelly donuts and 6 total donuts, we can keep track of the probability of choosing a donut with each 'draw':
1st donut = 3/6.... assuming he draws a jelly donut...
2nd donut = 2/5.... assuming he draws a jelly donut...
3rd donut = 1/4....

Thus, the probability of pulling the 3 jelly donuts is (3/6)(2/5)(1/4) = 6/120 = 1/20

Final Answer: D

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Rich
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by Jeff@TargetTestPrep » Thu Jun 28, 2018 6:31 am
AAPL wrote:Frank has a box containing 6 doughnuts: 3 jellies and 3 cinnamon twists. If Frank eat 3 doughnuts, chosen randomly from the box, what is the probability that he eats 3 jelly doughnuts?

A. 1/2
B. 1/3
C. 1/8
D. 1/20
E. 1/36
The number of ways to choose 3 doughnuts out of 6 is 6C3 = (6 x 5 x 4)/(3 x 2) = 20.

The number of ways of chose 3 jelly doughnuts out of 3 is 3C3 = 1.

Thus, the probability is 1/20.

Alternate Solution:

The probability of choosing the first jelly doughnut is 3/6; the probability that the next doughnut chosen is jelly is 2/5, and the probability that the third doughnut is jelly is 1/4. We multiply these probabilities to get 3/6 x 2/5 x 1/4 = 6/120 = 1/20.

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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