Question

A four-sided die is loaded in a way that each even face is twice as likely as each odd face. All even faces are equally likely, as are all odd faces. a. Construct a probabilistic model for a single roll of this die and find the probability that the outcome is no larger than 3. b. You are offered the following game: The entrance fee is $1 and this die is rolled 576 times with the number of times of observing a number less than or equal to two counted. If this number is more than 312 or less than 264, you win $10. 1. What is the distribution that Y, the number of times of observing a number less than or equal to two, is following? 2. Write down the exact formula for your probability of winning and losing. 3. Make your decision on whether to play or not and justify your answer by approximating the expected winning per game.

          A four-sided die is loaded in a way that each even face is twice as likely as each odd face. All even faces are equally likely, as are all odd faces.

a. Construct a probabilistic model for a single roll of this die and find the probability that the outcome is no larger than 3.

b. You are offered the following game: The entrance fee is $1 and this die is rolled 576 times with the number of times of observing a number less than or equal to two counted. If this number is more than 312 or less than 264, you win $10.

1. What is the distribution that Y, the number of times of observing a number less than or equal to two, is following?

2. Write down the exact formula for your probability of winning and losing.

3. Make your decision on whether to play or not and justify your answer by approximating the expected winning per game.

Added by Susan S.

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