Problem Solving

BTGmoderatorDC wrote:Two fair die with sides numbered 1 to 6 are tossed. What is the probability that the sum of the exposed faces on the die is a prime number?

A) 5/11
B) 5/12
C) 5/21
D) 2/9
E) 5/36

OA B

Source: Manhattan Prep

With two dies, we have 6*6 = 36 ways of getting a sum of 2 to 12. The prime numbers between 2 to 12 are 2, 3, 5, 7, and 11.

Number of ways of getting the sum, a prime number, is listed as

(1) Sum = 2: Ways: (1, 1): Total number of ways = 1;
(2) Sum = 3: Ways: (1, 2); (2, 1): Total number of ways = 2;
(3) Sum = 5: Ways: (1, 4); (2, 3); (3, 2);(4, 1): Total number of ways = 4;
(4) Sum = 7: Ways: (1, 6); (2, 5); (3, 4); (4, 3); (5, 2); (6, 1): Total number of ways = 6;
(5) Sum = 11: Ways: (5, 6); (6, 5): Total number of ways = 2

Total number of favorable ways = 1 + 2 + 4 + 6 + 2 = 15

Probability that the sum of the exposed faces on the die is a prime number = 15/36 = 5/12

The correct answer: B

Hope this helps!

-Jay
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BTGmoderatorDC wrote:Two fair die with sides numbered 1 to 6 are tossed. What is the probability that the sum of the exposed faces on the die is a prime number?

A) 5/11
B) 5/12
C) 5/21
D) 2/9
E) 5/36

OA B

Source: Manhattan Prep

The prime numbers between 2 and 12, inclusive, are 2, 3, 5, 7, and 11. The possible pairings with a sum being a prime number are:

(1,1), (2,1), (1,2), (1,4), (4,1), (3,2), (2,3), (4,3), (3,4), (6,1), (1,6), (2,5), (5,2), (6,5), (5,6)

So the probability is 15/36 = 5/12.

Answer: B