Three pennies are flipped. What is the probability that they all land with heads up?
(A) $\frac{1}{8}$
(B) $\frac{1}{6}$
(C) $\frac{1}{4}$
(D) $\frac{1}{3}$
(E) $\frac{1}{2}$
Three pennies are flipped. What is the probability that they all land with heads up?
(A) $\frac{1}{8}$
(B) $\frac{1}{6}$
(C) $\frac{1}{4}$
(D) $\frac{1}{3}$
(E) $\frac{1}{2}$

## Solution

If we toss one penny, the probability that it lands with heads up is $\frac{1}{2}$.

Since we want three heads up, we must multiply these probabilities together. That is, the probability is $\frac{1}{2} ¥ \frac{1}{2} ¥ \frac{1}{2}=\frac{1}{8}$.

Alternatively, we could list all of the possibilities for the 3 pennies, using $\mathrm{H}$ to represent heads and $\mathrm{T}$ to represent tails:

| HHH | THH |
| :--- | :--- |
| HHT | THT |
| HTH | TTH |
| HTT | TTT |

This means that there are 8 equally likely possibilities, one of which is the desired possibility.

Therefore, the probability of three heads coming up is $\frac{1}{8}$.

ANswer: (A)