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Use the following statement to answer parts ​a) and​ b). One hundred raffle tickets are sold for​ $3 each. One prize of ​$500 is to be awarded. Winners do not have their ticket costs of​ $3 refunded to them. Raul purchases one ticket.
​a) Determine his expected value.
​b) Determine the fair price of a ticket.

Respuesta :

Using the expected value of a discrete distribution, it is found that:

a) His expected value is of -$2.5.

b) The fair price of a ticket is of $0.5.

What is the mean of a discrete distribution?

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

In this problem, the distribution for the net value of the ticket is:

  • P(X = 497) = 1/1000.
  • P(X = -3) = 999/1000.

Item a:

The expected value is given by:

[tex]E(X) = 497\frac{1}{1000} - 3\frac{999}{1000} = -2.5[/tex]

His expected value is of -$2.5.

Item b:

With an unknown ticket price, the distribution is:

  • P(X = 500 - x) = 1/1000.
  • P(X = -x) = 999/1000.

The game is fair if E(X) = 0, hence:

[tex]\frac{500 - x}{1000} - \frac{999x}{1000} = 0[/tex]

0.5 - x = 0

x = 0.

The fair price of a ticket is of $0.5.

More can be learned about the expected value of a discrete distribution at https://brainly.com/question/24855677