Question

what is the probability of flipping three heads in a row with a fair coin?
a. $\frac{1}{4}$
b. $\frac{1}{8}$
c. $\frac{3}{8}$
d. $\frac{1}{2}$

Explanation:

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

For a fair coin, the probability of getting a head \( P(H)=\frac{1}{2} \).

Step2: Use the multiplication rule for independent events

Since the coin - flips are independent events, the probability of getting three heads in a row is \( P(H_1\cap H_2\cap H_3)=P(H_1)\times P(H_2)\times P(H_3) \).
Substitute \( P(H_1) = P(H_2)=P(H_3)=\frac{1}{2} \) into the formula: \( \frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8} \).

Answer:

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