Question

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

Explanation:

Step1: Determine single - flip probability

The probability of getting tails in a single fair - coin flip is $\frac{1}{2}$ since there are 2 possible outcomes (heads or tails) and 1 favorable outcome (tails).

Step2: Use the multiplication rule for independent events

Since the two coin - flips are independent events, the probability of two independent events $A$ and $B$ both 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 tails on the second flip. So $P(A) = P(B)=\frac{1}{2}$, and $P(A\cap B)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$