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? x 0 1 2 3 p(x) 1/4 1/4 1/4 1/4 x 1 2 3 4 5 6 7 8 p(x) 1 2/3 2/3 1/3 2/3 1/3 1/3 0 x 1 2 3 4 5 6 7 8 p(x) 0 1/3 1/3 2/3 1/3 2/3 2/3 1 x 0 1 2 3 p(x) 1/8 3/8 3/8 1/8

Explanation:

Step1: Count total outcomes

The sample - space $S$ has $n(S)=8$ elements.

Step2: Calculate $P(X = 0)$

The outcome with 0 heads is $TTT$. So $P(X = 0)=\frac{1}{8}$.

Step3: Calculate $P(X = 1)$

The outcomes with 1 head are $HTT$, $THT$, $TTH$. So $P(X = 1)=\frac{3}{8}$.

Step4: Calculate $P(X = 2)$

The outcomes with 2 heads are $HHT$, $HTH$, $THH$. So $P(X = 2)=\frac{3}{8}$.

Step5: Calculate $P(X = 3)$

The outcome with 3 heads is $HHH$. So $P(X = 3)=\frac{1}{8}$.

Answer:

$X$	0	1	2	3