Question

4. Two dice are thrown simultaneously. Find the probability of getting :
(i) an even number as the sum;
(ii) a total of at least 10;
(iii) same number on both dice i.e. a doublet;
(iv) a multiple of 3 as the sum.
(Hint : Elementary events associated to random experiment of throwing two dice are 36)​

Answer 1

Answer:

the sample space is (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)(4,5)(4,6)(4,4)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)

S(n)=36

first event=(1,2)(1,4)(1,6)(2,2)(2,4)(2,6)(3,2)(3,4)(3,6)(4,2)(4,4)(4,6)(5,2)(5,4)(5,6)(6,2)(6,4)(6,6)

n(P)=18

2-event=(4,6)(5,5)(6,4)(5,6)(6,5)(6,6)

n(p)=6

3-event=(1,1)(2,2)(3,3)(4,4)(5,5)(6,6)

n(p)=6

4-event=(1,2)(1,5)(2,1)(2,4)(3,3)(3,6)(4,2)(4,5)(5,1)(5,4)(6,3)(6,6)

n(p)=12