Question

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

Explanation:

Step1: Probability of single - coin flip

The probability of getting heads in a single fair - coin flip is $\frac{1}{2}$, since there are 2 possible outcomes (heads or tails) and only 1 favorable outcome (heads). So, $P(\text{head in 1 flip})=\frac{1}{2}$.

Step2: Use multiplication rule for independent events

Since the flips of the coins are independent events, the probability of multiple independent events occurring is the product of their individual probabilities. For 3 coin - flips, we multiply the probabilities of getting heads in each flip. So, $P(\text{heads, heads, heads})=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}$.

Step3: Calculate the product

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

Answer:

$\frac{1}{8}$