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 number of outcomes for each X value

• For \(X = 0\) (TTT), there is 1 outcome.
• For \(X = 1\) (HTT, THT, TTH), there are 3 outcomes.
• For \(X = 2\) (HHT, HTH, THH), there are 3 outcomes.
• For \(X = 3\) (HHH), there is 1 outcome.

Step2: Calculate probabilities

The total number of outcomes in the sample - space \(S\) is \(n(S)=8\).
The probability \(p(X)\) is given by \(p(X)=\frac{\text{Number of outcomes for a particular }X}{\text{Total number of outcomes}}\).

• \(p(X = 0)=\frac{1}{8}\)
• \(p(X = 1)=\frac{3}{8}\)
• \(p(X = 2)=\frac{3}{8}\)
• \(p(X = 3)=\frac{1}{8}\)

Answer:

\(X\)	0	1	2	3