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# Alex is playing a game of probability in which she rolls two dice. She

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Math Expert
Joined: 02 Sep 2009
Posts: 65807
Alex is playing a game of probability in which she rolls two dice. She  [#permalink]

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15 Apr 2018, 08:51
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45% (medium)

Question Stats:

67% (02:07) correct 33% (02:10) wrong based on 193 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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Posts: 2393
Re: Alex is playing a game of probability in which she rolls two dice. She  [#permalink]

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01 Jun 2020, 05:35
1
Bunuel wrote:
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

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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Re: Alex is playing a game of probability in which she rolls two dice. She  [#permalink]

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15 Apr 2018, 09:00
Bunuel wrote:
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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Re: Alex is playing a game of probability in which she rolls two dice. She  [#permalink]

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02 Jun 2020, 23:20
DavidTutorexamPAL wrote:
Bunuel wrote:
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
VP
Joined: 09 Mar 2016
Posts: 1261
Re: Alex is playing a game of probability in which she rolls two dice. She  [#permalink]

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13 Jul 2020, 07:06
Eduardo86 wrote:
DavidTutorexamPAL wrote:
Bunuel wrote:
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

Eduardo86 Since each die has 6 values, there are 6∗6=36 total combinations. When events are independent you multiply them
Re: Alex is playing a game of probability in which she rolls two dice. She   [#permalink] 13 Jul 2020, 07:06