Dice Probability...

[pkw209]

If a single die is rolled 3 times, what is the probability of rolling a 5 at least twice?

Answer to come...

[Testluv]

Hi Peter,

Assuming the die is fair, then the probability of rollng a 5 on one die toss is 1/6.

The probability of rolling a 5 at least twice means two 5s or three 5s.

How can we get two 5s?

In three ways: on the first and second tosses; on the first and third; or, on the second and third. (Rolling a 5 on two tosses means NOT rolling a 5 on one of the tosses, and the probability of that is 5/6):

(1/6)(1/6)(5/6) + (1/6)(5/6)(1/6) + (5/6)(1/6)(1/6)...or just: (1/6)(1/6)(5/6)*3 = 15/216.

And the probability of rolling a 5 on all three tosses is: (1/6)(1/6)(1/6) = 1/216 (and there's only one way to do that).

So: 15/216 + 1/216 = 16/216 = 2/27

[pkw209]

Thanks, Deepak. It's good to hear from you!