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

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

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New post 15 Apr 2018, 09:51
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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

The OA will be automatically revealed on Sunday 22nd of April 2018 09:51:48 AM Pacific Time Zone
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Re: Alex is playing a game of probability in which she rolls two dice. She [#permalink]

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New post 15 Apr 2018, 10:00
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] 15 Apr 2018, 10:00
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Alex is playing a game of probability in which she rolls two dice. She

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