Question

1. (5pts) the sample space for tossing three fair coins is {hhh, hht, hth, htt, thh, tht, tth, ttt}. what is the probability of exactly two heads?

Explanation:

Step1: Count favorable outcomes

The outcomes with exactly two heads are HHT, HTH, THH. So there are 3 favorable outcomes.

Step2: Count total outcomes

The sample - space has 8 total outcomes: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.

Step3: Calculate probability

The probability formula is $P(A)=\frac{n(A)}{n(S)}$, where $n(A)$ is the number of favorable outcomes and $n(S)$ is the number of total outcomes. So $P=\frac{3}{8}$.

Answer:

$\frac{3}{8}$