Consider the following game in a game arcade. The probability of winning a game is p and hence loosing the game is 1 − p. In order to win a prize you are given three choices: • A: win at least once in 6 games; • B: win at least twice in 12 games; and • C: win at least 3 times in 18 games. 1. If p = 1 6 which of A, B, or C should you choose to maximize your probability of winning the prize? You are required to compute the probabilities for each option to justify your answer. 2. Using the formulas derived in part (1), write a R-code to compute (not simulate) and plot the probability of winning the prize for options A, B, and C for different values of p varying from 0.1 to 0.9 in increments of 0.1. Summarize your observation. Regarding the plot: i) All three curves should be drawn in the same plot, ii) Make sure that the three curves are distinguishable (using different line styles, colors, and/or markers), and iii) make sure to add a legend that identifies the curves for the three different options (A, B, and C). Once you use the plot function, you can use lines to add lines to the plot. Also, use the legend function to add the legend.
Consider the following game in a game arcade. The
the game is 1 − p. In order to win a prize you are given three choices:
• A: win at least once in 6 games;
• B: win at least twice in 12 games; and
• C: win at least 3 times in 18 games.
1. If p = 1
6 which of A, B, or C should you choose to maximize your probability of winning the prize?
You are required to compute the probabilities for each option to justify your answer.
2. Using the formulas derived in part (1), write a R-code to compute (not simulate) and plot the probability
of winning the prize for options A, B, and C for different values of p varying from 0.1 to 0.9 in
increments of 0.1. Summarize your observation.
Regarding the plot: i) All three curves should be drawn in the same plot, ii) Make sure that the three
curves are distinguishable (using different line styles, colors, and/or markers), and iii) make sure to
add a legend that identifies the curves for the three different options (A, B, and C). Once you use the
plot
the legend.
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