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

Total number of outcomes when a coin is tossed 3 - times is $n(S)=2\times2\times2 = 8$.

Step2: Calculate probabilities for each $X$ value

For $X = 0$ (TTT), $p(X = 0)=\frac{1}{8}$; for $X = 1$ (HTT, THT, TTH), $p(X = 1)=\frac{3}{8}$; for $X = 2$ (HHT, HTH, THH), $p(X = 2)=\frac{3}{8}$; for $X = 3$ (HHH), $p(X = 3)=\frac{1}{8}$.

Answer:

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