The probability of picking the winning 4-digit number in a Pick 4 lottery is 1/10,000. Each play of the lottery is independent of the next play.

Question

(a) If you take a very large random sample of purchased lottery tickets, about 0.01% of the tickets will be winners. (True or False?)

(b) If 10,000 people play the Pick 4 lottery, exactly 1 person will win the lottery. (True or False?)

(c) The winning number in a Pick 4 lottery was 1234 two days in a row, therefore the likelihood of this number being picked again is much lower due to the Law of Averages. (True or False?)

Answer 1

a) turn 1/10000 into a decimal and see if it matches 0.01%. If it does, the answer will be "true," and if it doesn't then answer will be "false". --- note that 0.01% in decimal form is 0.0001.

b) This would only be true if people were not allowed to play the same number. People are free to choose independently of each other what number to play for the lottery. Therefore, 10,000 people playing does not guarantee a winner.

c) the chance of getting 1234 as the lottery number is 1/10000 every time the game is played. Because the games are independent of each other the outcome of one or two or a million games has no effect on the probabilities for the next game.

Let me know if this was helpful or if you need more clarification.

David