suppose a lottery game allows you to select a 2-digit number. Each digit may be either 1,2,3,4,5. if you pick the winning number you win $10 otherwise you win nothing A)what is the probability that you will pick the winning number B) the notation E(payoff)means the expected (or average)payoff. What is E(payoff) C)if the lottery tickets cost $1 how much should you expect to loose on the average per play
number of possible 2 digit numbers is
5x4 or 20
So the prob of a win is 1/20
E($10) = (1/20)(10) = .50 or 50 cents
So you would expect to lose 50 cents (or win 50 cents) on each $1 play.
A) To determine the probability of picking the winning number, we need to determine the total number of possible outcomes and the number of favorable outcomes.
In this case, we have 5 choices for the first digit and 5 choices for the second digit, giving us a total of 5*5 = 25 possible numbers.
Since there is only one winning number, the number of favorable outcomes is 1.
Therefore, the probability of picking the winning number is 1/25.
B) To calculate the expected payoff (E(payoff)), we multiply the payoff for each possible outcome by its corresponding probability and sum them up.
In this case, we have two possible outcomes: winning ($10 payoff) and not winning ($0 payoff).
The probability of winning is 1/25, and the probability of not winning is 24/25.
So the expected payoff is: (1/25) * $10 + (24/25) * $0 = $10/25 = $0.4.
Therefore, the expected payoff is $0.4.
C) To determine how much you should expect to lose on average per play, we subtract the expected payoff from the cost of the lottery ticket.
Since the lottery ticket costs $1 and the expected payoff is $0.4, the expected loss per play is $1 - $0.4 = $0.6.
Therefore, on average, you should expect to lose $0.6 per play.