When two dice are thrown simultaneously, the probability is n(S) = 6x6 = 36  Required, the sum of the two numbers that turn up is less than 12 That can be done as n(E) = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)(5,1), (5,2), (5,3), (5,4), (5,5), (5,6) (6,1), (6,2), (6,3), (6,4), (6,5) } = 35 Hence, required probability = n(E)/n(S) = 35/36. Hint: Find the sample space when two dice are thrown simultaneously. We have to find the probability of the pairs of two dice whose sum is less than 11. Using the sample space, find the favorable outcomes for sum less than 11. Complete Step by Step Solution: We are given in the question with the two dice and they are thrown simultaneously. Now, we have to find the total outcomes of the two dice when thrown simultaneously, it can also be said as sample space. There are 1, 2, 3, 4, 5 and 6 numbers in one dice. Since, there are two dice the sample space can be written as –$S = \left\{ (1,1)(1,2)(1,3)(1,4)(1,5)(1,6) \\ (2,1)(2,2)(2,3)(2,4)(2,5)(2,6) \\ (3,1)(3,2)(3,3)(3,4)(3,5)(3,6) \\ (4,1)(4,2)(4,3)(4,4)(4,5)(4,6) \\ (5,1)(5,2)(5,3)(5,4)(5,5)(5,6) \\ (6,1)(6,2)(6,3)(6,4)(6,5)(6,6) \\ \right\}$Number of total outcomes or sample space, $n(S) = 36$We have drawn the sample space when two dice are thrown simultaneously. From the question, we know that we have to find the probability of the two numbers whose sum is less than 11. Now, from the above sample space we have to find those pairs of dice whose sum is less than 11. Therefore, the favorable outcomes whose sum is less than 11 are –$E = \left\{ (1,1)(1,2)(1,3)(1,4)(1,5)(1,6) \\ (2,1)(2,2)(2,3)(2,4)(2,5)(2,6) \\ (3,1)(3,2)(3,3)(3,4)(3,5)(3,6) \\ (4,1)(4,2)(4,3)(4,4)(4,5)(4,6) \\ (5,1)(5,2)(5,3)(5,4)(5,5) \\ (6,1)(6,2)(6,3)(6,4) \\ \right\}$Number of favorable outcomes when two dice are thrown simultaneously whose sum is less than 11, $n\left( E \right) = 33$Now, we know that, probability is found by dividing the number of favorable outcomes by number of total outcomes –$P\left( E \right) = \dfrac{{n\left( E \right)}}{{n\left( S \right)}}$Putting the values in the above formula, we get –$ \Rightarrow P\left( E \right) = \dfrac{{33}}{{36}} \\ \Rightarrow P\left( E \right) = \dfrac{{11}}{{12}} \\ $Hence, $\dfrac{{11}}{{12}}$ is the required probability. Note: Total number of sample space can also be calculated by formula, ${m^n}$ , where, $m$ is the number of sides of dice or coin and $n$ is the number of coins or dice when thrown simultaneously. For example, two coins are thrown simultaneously, then, the number of sample space can be calculated as –$ \Rightarrow {2^2} = 4$ , as there are 2 sides in one – coin head and tail.No worries! We‘ve got your back. Try BYJU‘S free classes today! Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today!
Math Expert Joined: 02 Sep 2009 Posts: 86840
When two dice are thrown simultaneously, what is the probability that [#permalink]
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Question Stats: Hide Show timer StatisticsWhen two dice are thrown simultaneously, what is the probability that the sum of the two numbers that turn up is less than 11? A. 35/36B. 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]
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. 35/36B. 11/12 C. 5/6 D. 1/6 E. 1/12 cases when sum >11(5,6), ( 6,5), ( 6,6)3/36 = 1/12P ( sum <1) ; 1-1/12 = 11/12IMO B
e-GMAT Representative Joined: 04 Jan 2015 Posts: 3758
When two dice are thrown simultaneously, what is the probability that [#permalink]
Solution Given:
To find:
Approach and Working:
• Therefore, the probability that the sum of the two numbers that turn up < 11 =\(1 – (\frac{2}{6*6} + \frac{1}{6*6}) = 1 - \frac{3}{36} = 1 - \frac{1}{12} = \frac{11}{12}\) Answer: B
Manager Joined: 22 Sep 2018 Posts: 202
Re: When two dice are thrown simultaneously, what is the probability that [#permalink] I have a question regarding the order of the dice combinationsIf 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?
Manager Joined: 04 Feb 2018 Posts: 54
Re: When two dice are thrown simultaneously, what is the probability that [#permalink]
EgmatQuantExpert wrote: Solution Given:
To find:
Approach and Working:
• Therefore, the probability that the sum of the two numbers that turn up < 11 =\(1 – (\frac{2}{6*6} + \frac{1}{6*6}) = 1 - \frac{3}{36} = 1 - \frac{1}{12} = \frac{11}{12}\) Answer: B
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Re: When two dice are thrown simultaneously, what is the probability that [#permalink] 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. 35/36B. 11/12 C. 5/6 D. 1/6 E. 1/12All possibilities except (5,6) ; (6,5) ; (6,6) where the sum of two numbers is > 11Total possibilities, 6*6 =36, since with each number has 6 pairsThus P (A) = (36-3) /36 = 33/36 = 11/12 (Ans -B) _________________
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Re: When two dice are thrown simultaneously, what is the probability that [#permalink] Hello from the GMAT Club BumpBot!Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
Re: When two dice are thrown simultaneously, what is the probability that [#permalink] 28 Nov 2021, 17:25 |
When two dice are thrown simultaneously the probability that the sum of the two numbers that turn up is more than 11 is?
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