Question

You roll a normal 6-sided die. What is the probability of rolling at least one 5 if you roll 3 times?

Answer 1

Solution:
Number of possible cases of at least one 5 if you roll 3 times
1. One 5 while rolling 3 time
2. two 5 while rolling 3 time
3. Three 5 while rolling 3 time
Number of possible ways for One 5 = 3*(1 *5 *5) = 75
Number of possible ways for two 5 = 3*(1*1*5) = 15
Number of possible ways for three 5 = 1*1*1 = 1
Total number of ways to roll at least one 5 = 75 + 15 + 1 = 91
Total number of possible outcomes while rolling 3 die = 6 * 6 * 6 = 216
P(Rolling at least one 5) = Total number of ways to roll at least one 5/Total number of possible outcomes while rolling 3 dies = 91/216 = 0.4213
So there is 42.13% probability that at least one 5 if you roll 3 times.