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Bunuel
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Alex is playing a game of probability in which she rolls two dice. She 15 Apr 2018, 09:51
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C
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71% (02:08) correct 29% (02:21) wrong based on 590 sessions

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Alex is playing a game of probability in which she rolls two dice. She gets a point if the sum of the two dice is less than 8. What is the probability that she gains a point?

A. 5/12
B. 1/2
C. 7/12
D. 7/9
E. 3/4
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C
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Alex is playing a game of probability in which she rolls two dice. She 15 Apr 2018, 10:00
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Bunuel
Alex is playing a game of probability in which she rolls two dice. She gets a point if the sum of the two dice is less than 8. What is the probability that she gains a point?

A. 5/12
B. 1/2
C. 7/12
D. 7/9
E. 3/4
Show more

Since there are only a small number of options, we'll just list them.
This is an Alternative approach.

We'll list things systematically:
If the first roll is 1 we can get a sum of less than 8 with:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6): 6 options
If the first roll is 2 we can get a sum of less than 8 with:
(2,1), (2,2), (2,3), (2,4), (2,5): 5 options
If the first roll is 3 we have
(3,1), (3,2), (3,3), (3,4): 4 options
Similarly, if the first roll is 4 we have 3 options, if it is 5 we have 2 options and if it is 6 we have 1 option.
In total we have 6+5+4+3+2+1 = 21 options.
21/36 = 7/12 so (C) is our answer.
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Alex is playing a game of probability in which she rolls two dice. She 01 Jun 2020, 06:35
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Bunuel
Alex is playing a game of probability in which she rolls two dice. She gets a point if the sum of the two dice is less than 8. What is the probability that she gains a point?

A. 5/12
B. 1/2
C. 7/12
D. 7/9
E. 3/4
Show more

What kind of dice? The GMAT doesn't expect you to know anything about dice, so the question needs more detail.

Assuming the dice are numbered from 1 through 6, then no matter what number appears on the first die, it is always possible to get a sum of 7 if the second die displays the correct number. There's a 1/6 chance that will be true, so a 1/6 chance the sum is exactly '7'. The remaining 5/6 of the time, 1/2 the time the sum will exceed 7, and half the time it will be less than 7. So (5/6)(1/2) = 5/12 of the time, the sum is less than 7, and adding the 2/12 of the time the sum is precisely 7, there is a 7/12 probability the sum will be 7 or less.
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Alex is playing a game of probability in which she rolls two dice. She 03 Jun 2020, 00:20
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DavidTutorexamPAL
Bunuel
Alex is playing a game of probability in which she rolls two dice. She gets a point if the sum of the two dice is less than 8. What is the probability that she gains a point?

A. 5/12
B. 1/2
C. 7/12
D. 7/9
E. 3/4

Since there are only a small number of options, we'll just list them.
This is an Alternative approach.

We'll list things systematically:
If the first roll is 1 we can get a sum of less than 8 with:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6): 6 options
If the first roll is 2 we can get a sum of less than 8 with:
(2,1), (2,2), (2,3), (2,4), (2,5): 5 options
If the first roll is 3 we have
(3,1), (3,2), (3,3), (3,4): 4 options
Similarly, if the first roll is 4 we have 3 options, if it is 5 we have 2 options and if it is 6 we have 1 option.
In total we have 6+5+4+3+2+1 = 21 options.
21/36 = 7/12 so (C) is our answer.
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Hi can you explain to me how you get the 36?

Thanks so much
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Alex is playing a game of probability in which she rolls two dice. She 13 Jul 2020, 08:06
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Eduardo86
DavidTutorexamPAL
Bunuel
Alex is playing a game of probability in which she rolls two dice. She gets a point if the sum of the two dice is less than 8. What is the probability that she gains a point?

A. 5/12
B. 1/2
C. 7/12
D. 7/9
E. 3/4

Since there are only a small number of options, we'll just list them.
This is an Alternative approach.

We'll list things systematically:
If the first roll is 1 we can get a sum of less than 8 with:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6): 6 options
If the first roll is 2 we can get a sum of less than 8 with:
(2,1), (2,2), (2,3), (2,4), (2,5): 5 options
If the first roll is 3 we have
(3,1), (3,2), (3,3), (3,4): 4 options
Similarly, if the first roll is 4 we have 3 options, if it is 5 we have 2 options and if it is 6 we have 1 option.
In total we have 6+5+4+3+2+1 = 21 options.
21/36 = 7/12 so (C) is our answer.

Hi can you explain to me how you get the 36?

Thanks so much
Show more


Eduardo86 Since each die has 6 values, there are 6∗6=36 total combinations. When events are independent you multiply them :)
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Alex is playing a game of probability in which she rolls two dice. She 03 Jan 2025, 07:45
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Alex is playing a game of probability in which she rolls two dice.

As Alex is rolling two dice => Number of cases = \(6^2\) = 36

She gets a point if the sum of the two dice is less than 8. What is the probability that she gains a point?

P(Getting a point) = P(Sum < 8) = 1 - P(Sum ≥ 8)

Let's write down the cases in which Sum ≥ 8

Following are the cases
(2,6)
(3,5), (3,6)
(4,4), (4,5), (4,6)
(5,3), (5,4) ,(5,5), (5,6)
(6,2) till (6,6)

=> Total cases = 1 + 2 + 3 + 4 + 5 = \(\frac{5*6}{2}\) = 15

=> P(Sum ≥ 8) = \(\frac{15}{36}\) = \(\frac{5}{12}\)

=> P(Getting a point) = 1 - \(\frac{5}{12}\) = \(\frac{7}{12}\)

So, Answer will be C
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems

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