Four fair dices are thrown simultaneously. Find the probability that the highest number obtained is 4.

Explanation

4 must be obtained on at least one dice.
Let x be the number of dice on which 4 is obtained. The remaining dice will show number less than 4 which are 1, 2 and 3.
`therefore` Required probability
`= (.^(4)C_(1)xx3^(3))/(6^(4)) + (.^(4)C_(2)xx3^(2))/(6^(4)) + (.^(4)C_(3)xx3)/(6^(4))+(1)/(6^(4)) = (175)/(1296)`