Question

The Ohio lottery has a game called Pick 4 where a player pays $1 and picks a four-digit number. If
the four numbers come up in the order you picked, then you win $2700.
a) Write the probability distribution for a player's winnings.
Fill in the table below.
For the computer to grade this one correctly make sure that your X values are from
smallest to largest.
х
P(X)
b) What are your expected winnings?
Round final answer to 2 decimal places. Put correct units in the second box.
c) Which of the following is the correct interpretation of the expected winnings?

Answer 1

a) The probability distribution is:

$P(X = -1) = \frac{8999}{9000}$

$P(X = 2699) = \frac{1}{9000}$

b) The expected winnings are of -$0.7.

c) The interpretation is that for each game you play, you expect to lost $0.7.

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• A probability is the number of desired outcomes divided by the number of total outcomes.
• A probability distribution contains the probability of each outcome.

Item a:

• There are 9000 four-digit numbers.

Thus, the probability of you choosing the correct number, and thus earning $2699(discount of the price of $1), is:

$P(X = 2699) = \frac{1}{9000}$

An the probability of you choosing the wrong number, and thus paying $1, is:

$P(X = -1) = \frac{8999}{9000}$

Thus, the distribution is:

$P(X = -1) = \frac{8999}{9000}$

$P(X = 2699) = \frac{1}{9000}$

Item b:

• The expected winnings is the sum of each outcome multiplied by it's respective probability, thus:

$E = -\frac{8999}{9000} + 2700\frac{1}{9000} = \frac{-8999 + 2700}{9000} = -0.7$

The expected winnings are of -$0.7.

Item c:

The interpretation is that for each game you play, you expect to lost $0.7.

A similar problem is given at https://brainly.com/question/24855677