If a fair 6-side die is rolled three times, what is the

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

If a fair 6-side die is rolled three times, what is the

by BTGmoderatorLU » Sat Dec 28, 2019 4:30 pm

Source: Veritas Prep

If a fair 6-side die is rolled three times, what is the probability that exactly one 3 is rolled?

A. 25/216
B. 50/216
C. 25/72
D. 25/36
E. 5/6

The OA is C

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Source: Beat The GMAT — Problem Solving | Sat Dec 28, 2019 4:30 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Mon Dec 30, 2019 9:36 pm

BTGmoderatorLU wrote:Source: Veritas Prep

If a fair 6-side die is rolled three times, what is the probability that exactly one 3 is rolled?

A. 25/216
B. 50/216
C. 25/72
D. 25/36
E. 5/6

The OA is C

Say 3 comes up in the first roll, then the probability of getting exactly one 3 = 1/6*5/6*5/6 = 25/216;
Again, say 3 comes up in the second roll, then the probability of getting exactly one 3 = 5/6*1/6*5/6 = 25/216;
Again, say 3 comes up in the third roll, then the probability of getting exactly one 3 = 5/6*5/6*1/6 = 25/216;

Required probability = 3*25/216 = 25/72

The correct answer: C

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Jan 05, 2020 8:02 pm

BTGmoderatorLU wrote:Source: Veritas Prep

If a fair 6-side die is rolled three times, what is the probability that exactly one 3 is rolled?

A. 25/216
B. 50/216
C. 25/72
D. 25/36
E. 5/6

The OA is C

P(Exactly one three) = 1/6 x 5/6 x 5/6 = 25/216

The number of ways to select one 3 out of three rolls is YNN (or NYN or NNY) = 3!/2! = 3 ways.

So, the total probability is 3 x 25/216 = 75/216 = 25/72.

Answer: C

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