Question

A fair coin is flipped three times. What is the probability of getting heads at least twice? Write your answer as a simplified fraction.

Answer 1

You can use a Bernoulli Trial for this problem.
\[\left(\begin{matrix}n \\ r\end{matrix}\right)=p ^{r}\times q ^{n-r}\]
n is the amount of trials (coin flips) = 3
r is the result (2 OR 3) = 2/3
p is the probability of getting a head = 1/2
r is the probability of getting a tail = 1/2

We will have to do this twice, once for 2 heads and once for 3.
So we get:
\[\left(\begin{matrix}3 \\ 2\end{matrix}\right)\times (1/2)^{2} \times (1/2)^{3-2}\]
3 x 1/4 x 1/2 = 3/8
\[\left(\begin{matrix}3 \\ 3\end{matrix}\right)\times (1/2)^{3} \times (1/2)^{3-3}\]
1 x 1/8 x 1 = 1/8
3/8 + 1/8 = 1/2
So the probability of getting heads at least twice is 1/2

Answer 2

@tfitz17 perfect solution :)