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# When two dice are thrown simultaneously, what is the probability that

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Math Expert
Joined: 02 Sep 2009
Posts: 53006
When two dice are thrown simultaneously, what is the probability that  [#permalink]

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28 Jan 2019, 06:21
00:00

Difficulty:

35% (medium)

Question Stats:

45% (01:05) correct 55% (01:21) wrong based on 35 sessions

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When two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less than 11?

A. 35/36
B. 11/12
C. 5/6
D. 1/6
E. 1/12

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Re: When two dice are thrown simultaneously, what is the probability that  [#permalink]

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28 Jan 2019, 08:45
Bunuel wrote:
When two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less than 11?

A. 35/36
B. 11/12
C. 5/6
D. 1/6
E. 1/12

cases when sum >11
(5,6), ( 6,5), ( 6,6)
3/36 = 1/12
P ( sum <1) ; 1-1/12 = 11/12

IMO B
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Joined: 04 Jan 2015
Posts: 2577
When two dice are thrown simultaneously, what is the probability that  [#permalink]

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29 Jan 2019, 03:35

Solution

Given:
• Two dice are thrown simultaneously

To find:
• The probability that the sum of the two numbers that turn up < 11

Approach and Working:
• The probability that the sum of the two numbers that turn up < 11 = 1 – (the probability that the sum = 11 + the probability that the sum = 12)
• Therefore, the probability that the sum of the two numbers that turn up < 11 =$$1 – (\frac{2}{6*6} + \frac{1}{6*6}) = 1 - \frac{3}{36} = 1 - \frac{1}{12} = \frac{11}{12}$$

Hence, the correct answer is Option B

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Re: When two dice are thrown simultaneously, what is the probability that  [#permalink]

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30 Jan 2019, 20:04
I have a question regarding the order of the dice combinations

If the first dice rolls a 6 and the second dice rolls a 6, that is 1 combination greater than 11. However, doesn't that mean that we can reverse the order and get the same result?

Hence: 1/6 *1/6 *2 since they can be flipped. Why can we not do that and is there any material I can read to get a better grasp on this concept?
Re: When two dice are thrown simultaneously, what is the probability that   [#permalink] 30 Jan 2019, 20:04
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