Question

4 dice are rolled. Probability of not getting the same number on 3 dice.

Answer 1

Total number of outcome of each dice = 6

P(getting the same number as another throw) = 1/6

first of all Find the probability of getting 3 of the same number:

Probability of getting 2 of the dice the same as one of the other 2:

= 1 * 1 **1/6 * 1/6

= 1/36

now

Find the number of ways this can happen:

to get  Number of ways to get 3 out of the 4 dices the same :we will use combination formula

formula of combination= 4C3

combination= (4*3*2*1)/(3*2*1)

combination= 24/6=4

now Find the probability of getting 3 of the same:

P(3 of the same) = 1/36 * 4 = 1/9

Find the probability of NOT getting 3 of the same:

now subtract both

P(getting 3 NOT the same) = 1 - P(getting 3 of the same) = 1 - 1/9 = 8/9

hence  8/9 is the correct answer