a coin is tossed three times, with possible outcomes: {hhh, hht, hth, thh, htt, tht, tth, ttt}. identify the…
a coin is tossed three times, with possible outcomes: {hhh, hht, hth, thh, htt, tht, tth, ttt}. identify the graph of the probability distribution for the random variable representing the number of heads.
Answer
Explanation:
Step1: Count number of heads in each outcome
- For HHH: 3 heads.
- For HHT, HTH, THH: 2 heads.
- For HTT, THT, TTH: 1 head.
- For TTT: 0 heads.
Step2: Calculate probabilities
- Total number of outcomes $n = 8$.
- $P(X = 0)=\frac{1}{8}=0.125$ (1 outcome with 0 heads).
- $P(X = 1)=\frac{3}{8}=0.375$ (3 outcomes with 1 head).
- $P(X = 2)=\frac{3}{8}=0.375$ (3 outcomes with 2 heads).
- $P(X = 3)=\frac{1}{8}=0.125$ (1 outcome with 3 heads).
The correct probability - distribution graph should have bars at $x = 0,1,2,3$ with heights $0.125,0.375,0.375,0.125$ respectively. The given graph with equal - height bars at $x = 0,1,2,3$ with height $0.25$ is incorrect.