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

Explanation:

Step1: Determine probability of each flip

The probability of getting a tail on a fair - coin flip is $\frac{1}{2}$, and the probability of getting a head on a fair - coin flip is also $\frac{1}{2}$. The probability of getting a tail on the first flip, $P(T_1)=\frac{1}{2}$. The probability of getting a head on the second flip, $P(H_2)=\frac{1}{2}$. The probability of getting a tail on the third flip, $P(T_3)=\frac{1}{2}$.

Step2: Use the multiplication rule for independent events

Since the coin - flips are independent events, the probability of the combined event (tail on first, head on second, tail on third) is the product of the probabilities of each individual event. $P = P(T_1)\times P(H_2)\times P(T_3)$. $P=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8}$.

Answer:

$\frac{1}{8}$