Question

Many state lotteries have a game where the player chooses a three-digit number. When the winning number is drawn, any player who chooses exactly the same three-digit number wins a prize.

Mr. Cohen and Ms. Yang have a conversation about their lucky numbers. Mr. Cohen thinks that his number is a better number to play because the three digits are all different. Ms. Yang thinks that her number is a better number to play because the 1 digit is repeated. Is Mr. Cohen right? Is Ms. Yang right? What would you tell each of them about their chances of winning?

Answer 1

Both Mr. Cohen and Ms. Yang have the same chances of winning the lottery, regardless of their chosen numbers.Therefore, both Mr. Cohen and Ms. Yang have the same chances of winning the lottery, regardless of their chosen numbers.

Step-by-step explanation:

If the winning number is drawn at random, each possible three-digit number has an equal chance of being drawn. Therefore, the probability of any specific three-digit number being drawn is 1/1000, or 0.001.

Mr. Cohen believes that his number, with all three digits being different, is a better number to play.

However, this belief is incorrect. The probability of winning with a specific three-digit number where all digits are different is still 0.001, just like any other three-digit number.

Ms. Yang believes that her number, with one digit repeated, is a better number to play.

However, this belief is also incorrect. The probability of winning with a specific three-digit number where one digit is repeated is still 0.001, just like any other three-digit number.

Therefore, both Mr. Cohen and Ms. Yang have the same chances of winning the lottery, regardless of their chosen numbers.