Question

A die is rolled 13 times. what is the probability of at least two 2's appearing? (round your answer to four decimal places.)

Answer 1

Much easier to work with its complement. (Hint: when it says AT LEAST in probability, you should much rather work with the complementary pairing)


`\text{Pr(at least two 2's) = 1 - Pr(1 2) - Pr(no 2's)}`

`\text{Pr(1 2's)} = \binom{13}{1}\left( (1)/(6)^(1) \cdot (5)/(6)^(12)\right)`

`\text{Pr(no 2's)} = \left((5)/(6)\right)^(13)`


`\therefore \text{Pr(at least two 2's)} = 0.663530036... \text{ (by calculator work)}`