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. 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) 1/8 3/8 3/8 1/8 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) 1/4 1/4 1/4 1/4

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) 1/8 3/8 3/8 1/8 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) 1/4 1/4 1/4 1/4

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 (n(S)=8). The probability (p(X = k)=\frac{\text{Number of outcomes with }X = k}{n(S)}).

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