Question

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. coin toss 0.30 0.20 0.10 0.00 0 1 2 3 coin toss 0.40

Explanation:

Step1: Calculate probabilities for each number of heads

• Number of heads \(x = 0\): The outcome is \(TTT\). So \(P(X = 0)=\frac{1}{8}=0.125\)
• Number of heads \(x = 1\): The outcomes are \(HTT,THT,TTH\). So \(P(X = 1)=\frac{3}{8}=0.375\)
• Number of heads \(x = 2\): The outcomes are \(HHT,HTH,THH\). So \(P(X = 2)=\frac{3}{8}=0.375\)
• Number of heads \(x = 3\): The outcome is \(HHH\). So \(P(X = 3)=\frac{1}{8}=0.125\)

Answer:

The correct graph should have bars at \(x = 0\) with height \(0.125\), at \(x = 1\) with height \(0.375\), at \(x = 2\) with height \(0.375\), and at \(x = 3\) with height \(0.125\). (Since the options are not fully visible in text - but based on calculation this is the probability distribution)