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.