Three dice are rolled Find the probability of getting all si

Three dice are rolled. Find the probability of getting all sixes. (Enter your answer as a fraction.) Find the probability of getting all the same outcomes. (Enter your answer as a fraction.) Find the probability of getting all different outcomes. (Enter your answer as a fraction.)

Solution

Three Dices are rolled

Total events = 6^3

A.

favourable events = (6,6,6)

Total no. of favourable event = 1

Probability = Total no. of favourable event/Total events = 1/6^3

Probabilty = 1/216

B.

favourable events = (1,1,1), (2,2,2) ......(6,6,6)

Total no. of favourable event = 1

Probability = Total no. of favourable event/Total events = 6/6^3 = 1/36

Probabaility = 1/36

C.

first calculate probability if two or more outcomes are same.

favourable events = (1,1,1), (1,1,2) ......(1,1,6)

(2,2,1), (2,2,2)......(2,2,6)........(6,6,1), (6,6,2).......(6,6,6)

Total no. of favourable event = 36

Probability = Total no. of favourable event/Total events = 6/6^3 = 1/36

Probabaility = 1/36

Probability of getting all different outcomes = 1 - probability of getting two or more outcomes are same

Probability of getting all different outcomes = 1 - 1/36

Probability of getting all different outcomes = 35/36

Let me know if you have any doubts.