you flip a coin twice. what is the probability of getting tails and then getting tails? simplify your answer…

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 multiplication rule for independent events

Since the two coin flips are independent events, the probability of getting tails on the first flip and tails on the second flip is the product of the probabilities of getting tails on each individual flip. So, $P(\text{tails then tails})=\frac{1}{2}\times\frac{1}{2}$.

Step3: Calculate the result

$\frac{1}{2}\times\frac{1}{2}=\frac{1\times1}{2\times2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$