A six-sided die, with sides numbered 1 through 6, is rolled three times. What is the probability that the sum of the

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Thu Sep 10, 2020 12:54 am

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A six-sided die, with sides numbered 1 through 6, is rolled three times. What is the probability that the sum of the three rolls is at least 4?

A. $\dfrac1{216}$

B. $\dfrac1{54}$

C. $\dfrac12$

D. $\dfrac{53}{54}$

E. $\dfrac{215}{216}$

Answer: E

Source: Princeton Review

Source: Beat The GMAT — Problem Solving | Thu Sep 10, 2020 12:54 am

r3shabh: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Sat Sep 05, 2020 8:19 am

Re: A six-sided die, with sides numbered 1 through 6, is rolled three times. What is the probability that the sum of the

by r3shabh » Fri Sep 11, 2020 2:03 pm

By using property of probability
P(A) = 1-P(not A)
A = when sum of dices is at least 4
not A = sum is less than 4 . The only possible option in sum is 3 which is(1,1,1)
probability of (1,1,1) occurring P(not A) = \frac{1}{6} * \frac{1}{6} * \frac{1}{6} = \frac{1}{216}

P(A) = 1- \frac{1}{216} = \frac{215}{216}
E

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: A six-sided die, with sides numbered 1 through 6, is rolled three times. What is the probability that the sum of the

by Scott@TargetTestPrep » Mon Sep 14, 2020 4:08 am

Gmat_mission wrote: ↑
Thu Sep 10, 2020 12:54 am
A six-sided die, with sides numbered 1 through 6, is rolled three times. What is the probability that the sum of the three rolls is at least 4?

A. $\dfrac1{216}$

B. $\dfrac1{54}$

C. $\dfrac12$

D. $\dfrac{53}{54}$

E. $\dfrac{215}{216}$

Answer: E

Solution:

There are a total of 6 x 6 x 6 = 216 possible combinations when 3 dice are rolled. The only way that the sum is not at least 4 is if all 3 numbers rolled are 1 (notice that 1 + 1 + 1 = 3). Therefore, the probability that the sum is not at least 4 is 1/216, and thus, the probability that the sum is at least 4 is 1 - 1/216 = 215/216.

Answer: E

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