Question

what is the probability of obtaining three tails in a row when flipping a coin?
the probability of obtaining three tails in a row when flipping a coin is \boxed{}.
(type an integer or a simplified fraction.)

Explanation:

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

When flipping a fair coin, 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 coin - flips are independent events, and we want three tails in a row. If \(A\), \(B\), and \(C\) are independent events, \(P(A\cap B\cap C)=P(A)\times P(B)\times P(C)\). Here \(A\), \(B\), and \(C\) are the events of getting a tail in the first, second, and third flip respectively. So \(P(TTT)=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\).

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Answer:

\(\frac{1}{8}\)