Question

three coins are flipped. what is p(heads, heads, heads)?

Explanation:

Step1: Determine probability of one head

When flipping a fair coin, the probability of getting heads (H) is $P(H)=\frac{1}{2}$, and the same for tails (T).

Step2: Use independent events rule

Since each coin flip is an independent event, the probability of multiple independent events occurring together is the product of their individual probabilities. For three coin flips, the probability of getting heads on each flip is $P(H, H, H)=P(H)\times P(H)\times P(H)$.
Substituting $P(H)=\frac{1}{2}$ into the formula, we get $\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8}$.

Answer:

$\frac{1}{8}$