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Q.

Two dice are thrown simultaneously. Find the probability of getting the sum a prime number.


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a

512

b

572

c

582

d

532 

answer is A.

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Detailed Solution

Given, two dice are thrown simultaneously.
When 2 dice are thrown at the same time, the overall possible outcomes are,
(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)
Total number of possible outcomes n(S) = 36.
Sum of numbers 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)}.
Number of favourable outcomes n(A) = 15.
For an event A, the probability is given by,
PA=Number of favourable outcome n(A)Total number of outcomes n(S) The probability of getting the sum a prime number is,
PA=1536 ⇒P(A)=512 Thus, the probability of getting the sum a prime number is 512.
Hence, option 1 is correct answer.
 
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