Question

you flip a coin twice. what is the probability of getting tails and then getting tails? write your answer as a percentage rounded to the nearest tenth. %

Explanation:

Step1: Calculate the probability of getting tails in one flip

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 are interested in 1 outcome (tails).

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 tails on the first flip and tails on the second flip is \(P(T_1\cap T_2)=P(T_1)\times P(T_2)\).
Substitute \(P(T_1) = P(T_2)=\frac{1}{2}\) into the formula: \(P(T_1\cap T_2)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}\)

Step3: Convert the fraction to a percentage

To convert \(\frac{1}{4}\) to a percentage, we use the formula \(percentage=\frac{1}{4}\times100\%\).
\(\frac{1}{4}\times100\% = 25.0\%\)

Answer:

25.0%