Understanding Pick Four Lottery Game and Expected Net Gain

The video tutorial explains a pick four lottery game where players draw four numbered balls. It details the calculation of expected net gain from a one-dollar straight bet, considering the probabilities of winning and losing. The expected net gain is calculated using two methods: a direct approach and an alternative method involving multiple tickets. The tutorial concludes that the bet is not favorable due to a negative expected net gain.

How many possible selections are there in the Pick Four lottery game?

• 100,000

• 10,000

• 1,000,000

• 1,000

What is the payout for a successful one dollar straight bet in the Pick Four lottery?

• $100

• $500

• $4,500

• $5,000

What is the net gain if a player wins a straight bet?

• $4,499

• $4,500

• $5,000

• $5,499

What is the net gain if a player loses a straight bet?

• $1

• $0

• -$1

• -$10

What is the probability of winning a straight bet in the Pick Four lottery?

• 1 in 1,000

• 1 in 5,000

• 1 in 10,000

• 1 in 100,000

How is the expected net gain calculated?

• By adding the probabilities of winning and losing

• By multiplying the net gain by the probability of winning

• By subtracting the probability of losing from the probability of winning

• By taking the weighted average of net gains for winning and losing

What is the expected net gain per ticket in the Pick Four lottery?

• $0.55

• -$5.50

• -$0.55

• $5.50

If you buy 10,000 tickets, what is the expected net gain?

• $4,500

• -$4,500

• $0

• -$5,500

What is the alternative method to calculate the expected net gain?

• By changing the payout amount

• By considering the net gain for a single ticket

• By calculating the net gain for 10,000 tickets

• By using a different probability for winning

What is the overall assessment of the straight bet in the Pick Four lottery?

• It is a great bet

• It is a neutral bet

• It is not a great bet

• It is a guaranteed win