Question

question 9
when you flip a coin, what is the probability that it will come up tails twice in a row?
3/4
1
1/4
1/8
1/2

Explanation:

Step1: Calculate the probability of getting tails in one flip

When flipping a fair coin, the probability of getting tails in one 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 tails twice in a row 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: \(P(T_1\cap T_2)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}\)

Answer:

\(\frac{1}{4}\) (corresponding to the option \(1/4\))