Question

An unbased dice is rolled twice find the probability of getting the sum of two numbers is prime

Answer 1

Total Outcomes= 36. so probability of getting prime=13/36

Answer 2

The number of times dice rolled = 2.

Number of possible outcomes n(S) = 6 * 6

                                                            = 36.


Prime numbers from 1 to 12 are 2,3,5,7,11.

Let E1 be the event of getting the sum 2:

E1 = {1,1}

P(E1) = 1


Let E2 be the event of getting the sum 3.

n(E2) = {1,2}{2,1}

P(E2) = 2.


Let E3 be the event of getting the sum 5.

n(E3) = {1,4},{4,1},{2,3},{3,2}

P(E3) = 4.


Let E4 be the event of getting the sum 7.

n(E4) = {1,6},{6,1},{2,5},{5,2},{3,4},{4,3}

P(E4) = 6.



Let E5 be the event of getting the sum 11.

n(E5) = {5,6},{6,5}.

P(E5) = 2.



Therefore the probability p(E) = n(E)/n(S)

                                                  = 1 + 2 + 4 + 6 + 2/36

                                                  = 15/36

                                                  = 5/12.



Hope this helps!