Question

calculating the probability of independent events
three coins are flipped. what is p(heads, heads, heads)?

Explanation:

Step1: Determine probability of one head

The probability of getting a head when flipping a fair coin is $P(\text{head})=\frac{1}{2}$.

Step2: Use formula for independent events

For independent events $A$, $B$, $C$, $P(A\cap B\cap C)=P(A)\times P(B)\times P(C)$. Here, $A = B = C=\text{getting a head}$. So $P(\text{heads, heads, heads})=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}$.

Step3: Calculate the product

$\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1\times1\times1}{2\times2\times2}=\frac{1}{8}$.

Answer:

$\frac{1}{8}$