the sample space, $s$, of a coin being tossed three times is shown below, where $h$ and $t$ denote the coin…

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.\n$s = {hhh, hht, hth, htt, thh, tht, tth, ttt}$\nlet $x=$ the number of times the coin comes up heads. what is the probability distribution for the number of heads occurring in three coin tosses?

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.\n$s = {hhh, hht, hth, htt, thh, tht, tth, ttt}$\nlet $x=$ the number of times the coin comes up heads. what is the probability distribution for the number of heads occurring in three coin tosses?

Answer

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 }X}{\text{Total number of outcomes}}). So (p(0)=\frac{1}{8}), (p(1)=\frac{3}{8}), (p(2)=\frac{3}{8}), (p(3)=\frac{1}{8}).

Answer:

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