if you flip three fair coins, what is the probability that youll get a head on the first flip, a tail on the…

Explanation:

Step1: Determine probability of each flip

The probability of getting a head (H) or a tail (T) on a fair - coin flip is $\frac{1}{2}$. For the first flip, $P(H_1)=\frac{1}{2}$, for the second flip $P(T_2)=\frac{1}{2}$, and for the third flip $P(H_3)=\frac{1}{2}$.

Step2: Use the multiplication rule for independent events

Since coin - flips are independent events, the probability of the combined event $P(H_1\cap T_2\cap H_3)$ is the product of the probabilities of each individual event. So $P(H_1\cap T_2\cap H_3)=P(H_1)\times P(T_2)\times P(H_3)$. Substitute the values: $P(H_1)\times P(T_2)\times P(H_3)=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8}$.

Answer:

$\frac{1}{8}$