Question

If two dice are thrown simultaneously what is the probability of getting a 5 on both

please solve and send
answer should be 1/36​

Answer 1

In a throw of pair of dice, total no of possible outcomes=36(6×6) which 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)

Solution(i):

Let E be the event of not getting a 5 on either of the two dice

No. of favorable outcomes = 25

(i.e.,(1,1)(1,2)(1,3)(1,4)(1,6)(2,1)(2,2)(2,3)(2,4)(2,6)(3,1)(3,2)

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

P(E)=

36

25

Solution(ii):

Let E be the event of getting a 5 at least once

No. of favorable outcomes =11(i.e.,(1,5)(2,5)(3,5)(4,5)(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)(6,5)

P(E)=

36

11

Solution(iii):

Let E be the event of getting a 5 on both dice

No. of favorable outcomes =1(i.e.,(5,5)

P(E)=

36

1