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 \(P(T)=\frac{1}{2}\).

Step2: Use the multiplication rule for independent events

Since the two coin - flips are independent events (the outcome of the first flip does not affect the outcome of the second flip), the probability of getting heads first and then tails is \(P(H\cap T)=P(H)\times P(T)\).
Substitute \(P(H)=\frac{1}{2}\) and \(P(T)=\frac{1}{2}\) into the formula: \(P(H\cap T)=\frac{1}{2}\times\frac{1}{2}\).

Answer:

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