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bballgirl3230
Jan 14, 2007, 05:09 PM
a.) when rolling three dice, what is the probability of rolling at least one 1?
b.) when rolling three dice, what is the probability of rolling exactly one 1?

galactus
Jan 14, 2007, 05:26 PM
[QUOTE=bballgirl3230]a.) when rolling three dice, what is the probability of rolling at least one 1?
[quote]

Use the Binomial Distribution. Since it asks for at least one, you must add up the possibilities from 1 to 3.

\sum_{k=1}^{3}[C(3,k)p^{k}q^{3-k}]

where p=1/6 and q=5/6


For part b, just use it for the one case.

Elisha Grey
Jan 17, 2007, 10:10 AM
(a) The probability of getting no 1 is (5/6)^3, so the probability of getting at least one 1 is
1 - (5/6)^3

(b) The probability of getting a 1 on one particular die and not a 1 on the other two dice is
(1/6)(5/6)^2. Since there are three dice the probability of getting exactly one 1 is 3 times this, or 3(1/6)(5/6)^2.