you flip a coin twice. what is the probability of getting tails and then getting heads?

Explanation:

Step1: Probability of first - flip

The probability of getting tails on the first coin - flip is $\frac{1}{2}$ since a fair coin has 2 possible outcomes (heads or tails).

Step2: Probability of second - flip

The probability of getting heads on the second coin - flip is $\frac{1}{2}$ as well, because the two coin - flips are independent events.

Step3: Use the multiplication rule for independent events

For independent events $A$ and $B$, the probability of $A$ and $B$ occurring is $P(A\cap B)=P(A)\times P(B)$. Here, $A$ is the event of getting tails on the first flip and $B$ is the event of getting heads on the second flip. So $P = \frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$