Question

You flip three coins. What is the probability that you get at least two tails, given that you get at least one tail?

Answer 1

It's heads or tails, so it's a binomial distribution. So we use the formula: \[{n \choose r}{p^r}{(1-p)^{n-r}}\] where n is the number of trials (3) and r is the number of successes (tails).
\[{3 \choose 2}{0.5^2}{(1-0.5)^{3-2}}={3 \choose 2}{(0.25)}{(0.5)}={3 \choose 2}(0.125)\]
\[{n \choose r}={n! \over {r!(n-r)!}}={3! \over 2!1!}={{1*2*3} \over 1*2*1}=3\]
So, \[3*0.125=0.375=P(X=2)\]