if you flip three fair coins, what is the probability that youll get heads on the first two flips and tails…

Explanation:

Step1: Determine probability of each flip

The probability of getting heads (H) or tails (T) on a fair - coin flip is $\frac{1}{2}$.

Step2: Use the multiplication rule for independent events

Since coin - flips are independent events, if $A$, $B$, and $C$ are the events of getting heads on the first flip, heads on the second flip, and tails on the third flip respectively, then $P(A\cap B\cap C)=P(A)\times P(B)\times P(C)$. $P(A)=\frac{1}{2}$, $P(B)=\frac{1}{2}$, $P(C)=\frac{1}{2}$. So $P(A\cap B\cap C)=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8}$.

Answer:

$\frac{1}{8}$