Understanding Lottery Game and Expected Value

The video tutorial explains a lottery game where Ahmed picks two numbers and a letter. The video defines a random variable X representing the net profit from playing the game. It calculates the expected value of Ahmed's ticket, 04R, by considering the probabilities of winning the grand prize, the small prize, or losing. The expected net profit is calculated to be $2.81, which is unusual for a lottery game as it offers a positive expected return for the player.

What is the cost for Ahmed to play the lottery game?

• $1

• $10

• $5

• $100

What does Ahmed need to match to win the grand prize?

• Two numbers and one letter in order

• Only one number

• Only one letter

• Two letters and one number

What is the random variable X defined as in the context of the lottery game?

• The number of tickets sold

• The net profit from playing

• The number of prizes available

• The total cost of playing

How is the expected value of the lottery game calculated?

• By subtracting the cost of playing from the prize

• By multiplying the probability of each outcome by its net profit

• By adding the probabilities of all outcomes

• By dividing the total prize by the number of players

What is the probability of winning the grand prize?

• 1 in 1000

• 1 in 10000

• 1 in 5000

• 1 in 2600

What must be subtracted from the probability of getting the letter right to find the probability of the small prize?

• Probability of getting both numbers wrong

• Probability of getting one number right

• Probability of losing

• Probability of the grand prize

What is the probability of losing the game?

• 1 in 26

• 1 in 10

• 25 in 26

• 1 in 100

What is the expected net profit from playing the lottery game?

• $5.00

• $2.81

• $0.00

• $10.00

Why is this lottery game considered unusual?

• It has a positive expected net profit for the player

• It is free to play

• It has a negative expected net profit

• It has no prizes

Who typically has the expected net profit in most lottery games?

• The player

• The state or casino

• The prize winner

• The ticket seller