Question

what is the probability of obtaining two tails in a row when flipping a coin? the probability of obtaining two tails in a row when flipping a coin is (type an integer or a simplified fraction)

Explanation:

Step1: Determine the probability of getting a tail in one flip

When flipping a fair coin, there are 2 possible outcomes (head or tail). The probability of getting a tail 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), if \(A\) and \(B\) are independent events, \(P(A\cap B)=P(A)\times P(B)\). Let \(A\) be the event of getting a tail on the first flip and \(B\) be the event of getting a tail on the second flip. Then \(P(A) = P(B)=\frac{1}{2}\), and \(P(A\cap B)=\frac{1}{2}\times\frac{1}{2}\).

Answer:

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