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: Calculate the probability of getting heads

The probability of getting heads in a single coin - flip is \(P(H)=\frac{1}{2}\) since there are 2 possible outcomes (heads or tails) and we want 1 of them (heads).

Step2: Calculate the probability of getting tails

The probability of getting tails in a single coin - flip is \(P(T)=\frac{1}{2}\) since there are 2 possible outcomes (heads or tails) and we want 1 of them (tails).

Step3: 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 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:

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