Probability!

Question

4. In the old days, slot machines worked like this: you pull the lever to spin three wheels; each wheel has 20 symbols, all equally likely to show when the wheel stops spinning. The three wheels are independent of each other. Suppose that the middle wheel has nine cherries among its 20 symbols and the left and right wheels have one cherry each. You win the Jackpot if all three wheels show cherries. What is the probability of winning the Jackpot? 0.001125

 

5. In Ohio’s Pick 4 game, you pay $1 to select a sequence of four digits, from 0 to 9. Numbers can repeat. If you buy one ticket and win, you get $5000.

 

 

a. What is the probability of winning? Hint: the range of winning numbers goes from 0000 to 9999. 

b. What is the expectation of this game?

Answer 1

4. If the wheels are independent the probabilities are multiplicative.

so take 1/20 times 9/20 times 1/20, and we get 9/20^3, or 9/8000=.001125, as you wrote above

 

5. If we can repeat digits, then as the hint suggests we are choosing a four digit number between 0000 and 9999 (the keyword sequence in the problem indicates that the order definitely matters, i.e. 1234 is a different lotto ticket than 4321).

 

How many numbers are there from 0000 to 9999, the probability of winning is 1 in that number.

 

The expectation (after the ticket is purchased) is the prize for winning times the probability of winning...it should be 1/2 or $.50....

 

How much should I expect to lose for each $1 ticket I purchase? Should we factor in the cost of the ticket into the calculation for expectation?  Should this be positive or negative?  Is this a game we should be playing?