Consider the following experiment: 0. Set the counter n to 1. 1. Toss a fair coin and record the result. Then, • if it comes up heads, toss the coin once more and record the result, then end the experiment; • if it comes up tails and n ≤ 4, add 1 to n and repeat step 1; • if it comes up tails and n = 5, end the experiment. 1. Draw the complete tree diagram for this experiment.
Consider the following experiment:
0. Set the counter n to 1.
1. Toss a fair coin and record the result. Then,
• if it comes up heads, toss the coin once more and record the result, then end the experiment;
• if it comes up tails and n ≤ 4, add 1 to n and repeat step 1;
• if it comes up tails and n = 5, end the experiment.
1. Draw the complete tree diagram for this experiment.
2. What are the sample space and probability function of this experiment?
3. What is the probability that . . .
a. the final toss is a tail?
b. the next-to-last toss is a head?
The random variable X counts the number of tosses made in this experiment.
4. What are the possible values of X and the probabilities that each will occur?
5. What is the probability that . . .
a. X is an even number?
b. X is at least four?
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