Question

you flip a coin twice. what is the probability of getting heads and then getting tails? simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Determine the probability of each event

The probability of getting heads in a single coin - flip is \(P(H)=\frac{1}{2}\), and the probability of getting tails in a single coin - flip is \(P(T)=\frac{1}{2}\).
Since the two coin - flips are independent events (the outcome of the first flip does not affect the outcome of the second flip), we use the formula for the probability of independent events \(P(A\cap B)=P(A)\times P(B)\).
Let \(A\) be the event of getting heads and \(B\) be the event of getting tails.

Step2: Calculate the combined probability

We substitute \(P(A)=\frac{1}{2}\) and \(P(B)=\frac{1}{2}\) into the formula \(P(A\cap B)\):
\(P(H\cap T)=\frac{1}{2}\times\frac{1}{2}\)

$$P(H\cap T)=\frac{1\times1}{2\times 2}=\frac{1}{4}$$

Answer:

\(\frac{1}{4}\)