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If two fair six-sided dice are thrown, what is the probability that th
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15 Sep 2021, 01:21
15 Sep 2021, 01:21
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If two fair six-sided dice are thrown, what is the probability that the sum of the numbers showing on the dice is a multiple of 3 ?
(A) 1/4
(B) 3/11
(C) 5/18
(D) 1/3
(E) 4/11
(A) 1/4
(B) 3/11
(C) 5/18
(D) 1/3
(E) 4/11
Re: If two fair six-sided dice are thrown, what is the probability that th
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15 Sep 2021, 07:51
15 Sep 2021, 07:51
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The Sample space is (1,1),...*6,6) = 36.
Favourable outcomes = (2,1),(1,2), (5,1),(4,2),(3,3),(2,4),(1,5), (6,3),(5,4),(4,5),(3,6) and (6,6).
In short, minimum is 3 and max is 12 and how many ways to get them in a 2 dices.
So = 12/36 = 1/3 D)
Favourable outcomes = (2,1),(1,2), (5,1),(4,2),(3,3),(2,4),(1,5), (6,3),(5,4),(4,5),(3,6) and (6,6).
In short, minimum is 3 and max is 12 and how many ways to get them in a 2 dices.
So = 12/36 = 1/3 D)
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Re: If two fair six-sided dice are thrown, what is the probability that th
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15 Oct 2022, 09:52
15 Oct 2022, 09:52
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Given that two fair six-sided dice are thrown and we need to find what is the probability that the sum of the numbers showing on the dice is a multiple of 3 ?
As we are rolling two dice => Number of cases = \(6^2\) = 36
Multiple of three between 1+1 (=2) and 6+6(=12) are 3, 6, 9 , 12
Lets start writing the possible cases where sum of the two rolls = 3, 6, 9, 12. Following are the possible cases:
(1,2), (1,5)
(2,1), (2,4)
(3,3), (3,9)
(4,2), (4,5)
(5,1), (5,4)
(6,3), (6,6)
=> 12 cases
=> Probability that sum of two rolls is a multiple of 3 = \(\frac{12}{36}\) = \(\frac{1}{3}\)
So, Answer will be D
Hope it helps!
Watch the following video to learn How to Solve Dice Rolling Probability Problems
As we are rolling two dice => Number of cases = \(6^2\) = 36
Multiple of three between 1+1 (=2) and 6+6(=12) are 3, 6, 9 , 12
Lets start writing the possible cases where sum of the two rolls = 3, 6, 9, 12. Following are the possible cases:
(1,2), (1,5)
(2,1), (2,4)
(3,3), (3,9)
(4,2), (4,5)
(5,1), (5,4)
(6,3), (6,6)
=> 12 cases
=> Probability that sum of two rolls is a multiple of 3 = \(\frac{12}{36}\) = \(\frac{1}{3}\)
So, Answer will be D
Hope it helps!
Watch the following video to learn How to Solve Dice Rolling Probability Problems
