Question

To simulate a toss of a coin, we let the digits 0, 1, 2, 3, and 4 correspond to a head and the digits 5, 6, 7, 8, and 9 correspond to a tail. Consider the following game: We are going to toss the coin until we either get a head or we get two tails in a row, whichever comes first. If it takes us one toss to get the head, we score 2 points. If it takes us two tosses, we score 1 point. If we get two tails in a row, we score 0. Use the following sequence of random digits to simulate this game as many times as possible: 12975 13258 45144.

A. Based on your simulation, what is the estimated probability of scoring zero?

Answer 1

To simulate the given game, we need to follow the rules mentioned and use the given sequence of random digits. Based on the simulation, the estimated probability of scoring zero points in this particular game is 1.

Step-by-step explanation:

To simulate the given game, we need to follow the rules mentioned. We toss the coin until we either get a head or two tails in a row. If it takes one toss to get the head, we score 2 points. If it takes two tosses, we score 1 point. If we get two tails in a row, we score 0. Now, let's simulate the game using the given sequence of random digits:

Simulation:

1. 
   
3. First toss: 1 (heads). Score: 2 points.
4. 
   
6. Second toss: 2 (heads). Score: 2 points.
7. 
   
9. Third toss: 9 (tails). Score: 0 points. Game ends.

Based on the simulation, we scored 0 points once in this particular game. To estimate the probability of scoring zero, we need to repeat this simulation many times and calculate the frequency of scoring zero points. Since the given sequence of random digits is limited, we can only simulate the game once with it. To get a more accurate estimation of the probability, we would need a larger sample size.