Question

Two unbiased dice are thrown simultaneously. what is the probability of getting at most one five in a single throw of the two dice?

Answer 1

Let S be sample space
n(S) = no. of combinations when 2 dice are rolled.
n(S) = 6² = 36


E be the Event of getting sum at most 5

n(E) = no. of ways of getting sum atmost 5

Possible Cases for sum__Possible Combinations

2 (min. sum)____(1, 1)
3 ____________(1,2), (2,1)
4 ____________(1,3), (2,2), (3,1)
5 ____________(1,4), (2,3), (3,2), (4,1)


n(E) is nothing but the no. of these combinations.
n(E)= 1 + 2 + 3 + 4= 10

Probability = n(E) / n(S)

Required probability = 10 / 36 = 5/18


;)
Hope it helps you..

Answer 2

Answer:

Step-by-step explanation:

Let S be sample space

n(S) = no. of combinations when 2 dice are rolled.

n(S) = 6² = 36

E be the Event of getting sum at most 5

n(E) = no. of ways of getting sum atmost 5

Possible Cases for sum__Possible Combinations

2 (min. sum)____(1, 1)

3 ____________(1,2), (2,1)

4 ____________(1,3), (2,2), (3,1)

5 ____________(1,4), (2,3), (3,2), (4,1)

n(E) is nothing but the no. of these combinations.

n(E)= 1 + 2 + 3 + 4= 10

Probability = n(E) / n(S)

Required probability = 10 / 36 = 5/18