Q. 115.0( 4 Votes )

Two dice are thro

Answer :

Given: Two dice are thrown at the same time and the product of numbers appearing on them is noted.


To find: the probability that the product is a prime number.


Explanation:

Total number of outcomes of one dice = 6


So the total number of outcomes of two dices = 6 × 6

= 36


So, n(S) = 36


And all the outcomes of S are


S = {(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)}


Let E denote outcomes such that the product is prime (i.e., having only factors), then the favorable outcomes of event E are


E = {(1,2), (1,3), (1,5), (2,1), (3,1), (5,1)}


Hence the number of outcomes of E is n(E) = 6


Hence the probability that the product is a prime number is


P (getting the product is a prime number)


Substituting corresponding values, we get




Hence the probability that the product is a prime number is .

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