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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.