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01 Jul 2021, 04:15
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C
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A cube with its sides numbered 1— 6 is rolled twice, first landing on a and then landing on b. If any roll of the cube yields an equal chance of landing on any of the numbers 1 — 6, what is the probability that a + b is prime?
A) 0
B) \(\frac{1}{12}\)
C) \(\frac{5}{12}\)
D) \(\frac{7}{18}\)
E) \(\frac{4}{9}\)
A) 0
B) \(\frac{1}{12}\)
C) \(\frac{5}{12}\)
D) \(\frac{7}{18}\)
E) \(\frac{4}{9}\)
01 Jul 2021, 09:00
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Bunuel
The prime numbers are 2, 3, 5, 7, and 11. Let's not forget there are 6*6 = 36 rolls in total.
2 can be built from 1 + 1 only.
3 = 1 + 2 or 2 + 1. 2 rolls.
5 = 1 + 4 through 4 + 1 which is 4 rolls.
7 = 1 + 6 through 6 + 1 which is 6 rolls.
11 = 5 + 6 or 6 + 5. 2 rolls.
In total that is 1 + 2 + 4 + 6 + 2 = 15 rolls out of 36. \(\frac{15}{36} = 5/12\).
Ans: C
15 Oct 2022, 23:12
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Given that A cube with its sides numbered 1 through 6 is rolled twice, first landing on a and then landing on b. and We need to find If any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6, what is the probability that a + b is prime?
As we are rolling the cube twice => Number of cases = \(6^2\) = 36
First roll gives a and second roll gives b and we need to find the Probability that a+b is prime => Sum of the two rolls is prime
We know that out of the numbers from 2(1+1) to 12 (6+6) we have only five prime numbers and they are 2, 3, 5, 7 and 11
(Watch this video if you are not aware of Prime Numbers)
Following are the possible cases in which sum of the two rolls is a prime number
(1,1), (1,2), (1,4), (1,6)
(2,1), (2,3), (2,5)
(3,2), (3,4)
(4,1), (4,3)
(5,2), (5,6)
(6,1), (6,5)
=> 15 possibilities
=> Probability that a + b is prime = \(\frac{15}{36}\) = \(\frac{5}{12}\)
So, Answer will be C
Hope it helps!
Watch the following video to learn How to Solve Dice Rolling Probability Problems
As we are rolling the cube twice => Number of cases = \(6^2\) = 36
First roll gives a and second roll gives b and we need to find the Probability that a+b is prime => Sum of the two rolls is prime
We know that out of the numbers from 2(1+1) to 12 (6+6) we have only five prime numbers and they are 2, 3, 5, 7 and 11
(Watch this video if you are not aware of Prime Numbers)
Following are the possible cases in which sum of the two rolls is a prime number
(1,1), (1,2), (1,4), (1,6)
(2,1), (2,3), (2,5)
(3,2), (3,4)
(4,1), (4,3)
(5,2), (5,6)
(6,1), (6,5)
=> 15 possibilities
=> Probability that a + b is prime = \(\frac{15}{36}\) = \(\frac{5}{12}\)
So, Answer will be C
Hope it helps!
Watch the following video to learn How to Solve Dice Rolling Probability Problems
