Probability of Rolling 2 At Least Twice

Date: Wed, 3 Jul 1996 18:22:11 -0400 (EDT) 
From: Anonymous
Subject: probability of rolling 2 twice

A fair die is rolled three times. Find the probability of rolling a 
"two" at least twice.

Thanking you ahead of time, Dr. Math.

Date: Thu, 4 Jul 1996 12:43:49 -0400 (EDT) 
From: Dr. Anthony
Subject: Re: probability of rolling 2 twice

At least twice means two OR three times. We use the binomial 
probability distribution, with p (probability of success)= 1/6, 
q (probability of failure) = 5/6 and n (number of trials) = 3 

P(2) = 3_C_2*(1/6)^2*(5/6) = 3*(1/36)*(5/6) = 15/216 

P(3) = 3_C_3*(1/6)^3*(5/6)^0 = 1*1/216*1 = 1/216 

So P(2) + P(3) = 16/216 = 2/27

-Doctor Anthony, The Math Forum