Question

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

Explanation:

Step1: Probability of one head

A fair coin has 2 outcomes (heads or tails). So the probability of getting heads for one coin flip is $P(\text{heads}) = \frac{1}{2}$.

Step2: Probability of three independent heads

Since the coin flips are independent events, the probability of multiple independent events occurring together is the product of their individual probabilities. For three coin flips, we calculate $P(\text{heads, heads, heads}) = P(\text{heads}) \times P(\text{heads}) \times P(\text{heads})$. Substituting the value of $P(\text{heads}) = \frac{1}{2}$, we get $\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}$.

Answer:

$\frac{1}{8}$