Question

the sample space, s, of a coin being tossed three times is shown below, where h and t denote the coin landing on heads and tails respectively. s = {hhh, hht, hth, htt, thh, tht, tth, ttt} let x = the number of times the coin comes up heads. what is the probability distribution for the number of heads occurring in three coin tosses?

Explanation:

Step1: Count total outcomes

The sample - space $S=\{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$, so $n(S)=8$.

Step2: Calculate probabilities for each value of $X$

• When $X = 0$ (no heads, i.e., $TTT$), $P(X = 0)=\frac{1}{8}$.
• When $X = 1$ (one head: $HTT,THT,TTH$), $P(X = 1)=\frac{3}{8}$.
• When $X = 2$ (two heads: $HHT,HTH,THH$), $P(X = 2)=\frac{3}{8}$.
• When $X = 3$ (three heads: $HHH$), $P(X = 3)=\frac{1}{8}$.

Answer:

$X$	$P(X)$
1	$\frac{3}{8}$
2	$\frac{3}{8}$
3	$\frac{1}{8}$