Calculating Expected Values

Given the probability model in the table below, what is the expected value of the random variable?
  X        50          20        5
P(X)     0.1         0.3      0.6

• 14
• 4.67
• 5
• 7.5

If the expected value is negative, are you expected to win?

• yes
• no

A coin is flipped 3 times. If you get tails once you get $5, tails twice you get $15, and tails on all three flips you get $40. What is the expected amount of money you will get?

• $12.50
• $5
• $7.50
• $10

Eva flips a coin. If she gets heads, she wins $4. If she gets tails, she loses $3. What is her expected value of a coin flip?

• $1

• $0.50

• -$0.50

• $0

Suppose you pay $1.00 to roll a fair die with the understanding you will get $3.00 back rolling a 4 or a 2, and nothing otherwise. Is this a fair game?

• yes

• no

Suppose you buy a ticket for $6 out of a lottery of 1000 tickets where the prize for the one winning is to be $800. What is the expected return from this lottery (after paying for it)?

• $800

• -$6.50

• -$6

• -$5.20

Choose an American household at random. What is the expected number of cars for that household?

• 1.75
• 1.84
• 2.00
• 2.50

A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution. What is the average number of customers that the owner can expect to make a purchase in the first hour of opening?

• 0.2

• 1.4

• 2.0

• 3.0

The following table shows the probability distribution for the number of children in each family in the town of Crossville. What is the average number of children in this town?

• 1.9

• 0.3

• 2.1

• 3

You pick a card from a deck.  If you get a face card, you win $5.  If you get an ace, you win $30 plus an extra $60 for the ace of hearts.  For any other card you win nothing. Find the expected value you will win.

• $5.00
• $3.85
• $4.04
• $4.62