A die is rolled 10 times Find the probability of rolling exa

A die is rolled 10 times. Find the probability of rolling exactly 1 five

The probability is

...

(Round to four decimal places as needed.)

Solution

A die is rolled 10 times. We need to find the rolling exactly 1 five

The probability of rolling a number 5  =1/6

This is a binomial distribution. The probability of rolling a number other than a 5 is 5/6. So the various probabilities are given by the expansion of

{ (5/6) + (1/6) }^10 = (5/6)^10+ 10 (5/6)^9 (1/6) + ..+ . . . . etc.

(5/6)^10 is the probability of rolling other than a five on all 10 rolls.

10 (5/6)^9 (1/6) is the probability of rolling just one 1 five, so is the answer to the question by

= 10 x 5^9 / 6^10

= 0.32