1. Carlton is playing a coin toss game in which he tries to guess as many correc

Question

1. Carlton is playing a coin toss game in which he tries to guess as many correct outcomes as possible out of 5 tosses of the coin. He decides to guess "heads" for every toss of the coin. Is Carlton's decision an optimal decision?

a) Yes

b) No

2. According to the table. Carlton needed some guidance for his coin toss game, so he opened Excel and simulated the outcome 1000 times. The table above shows the number of times the simulation yielded a certain number of "heads" coin tosses out of 5 coin tosses. What is the simulated probability that Carlton gets no coin tosses correct?

3. Again, referring to Carlton's coin toss game (and the simulation resutls table shown above) what is the simulated probability that Carlton is correct AT LEAST 4 times?

4. In Carlton's coin toss game simulation, what is the simulated average number of "heads" outcomes out of 5 tosses of the coin?

5. The rules of Carlton's coin toss game are now changed. From now on, he only gets another toss if he is correct on the current toss. He still gets at most 5 coin tosses. Is the expected number of "heads" in this game higher or lower than in the game according to the original rules?

a) The expected number of "heads" tossed is higher

b) The expected number of "heads" tossed is lower

c) The expected numer of "heads" tossed is the same

d) We don't have enough information to tell

Explanation / Answer

1. Yes Carlton's decision is optimal

Because the probability of getting head on a toss of fair coin is 0.5 which is equal to the probability of getting tail.

Both the choices Head or Tail would be optimal

Please provide the table data to solve the question further

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