Diced up
Probability
Level
3
When rolling a fair 6-sided die (with numbers 1, 2, 3, 4, 5, 6 on it) 5 times, what are the chances of rolling at least 2 sixes?
Express your answer as a percentage.
The answer is 19.62.
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1 solution
Moderator note:
Sometimes, counting by the complement is much easier!
The chance of at least 2 sixes = 1 - (chance of at most 1 six.)
Chance of zero sixes = 5/6 * 5/6 * 5/6 * 5/6 * 5/6 = 3125/7776
Chance of exactly one six = 5 * (1/6 * 5/6 * 5/6 * 5/6 * 5/6) = 3125/7776
Chance of at most one six = (3125 + 3125)/7776 = 6250/7776
Chance of at least 2 sixes = (7776-6250)/7776 = 1526/7776 = 0.1962 = 19.62%