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 says that his "lucky number" is 247. He buys a lottery ticket with this number. What is the probability that Mr. Cohen will win a prize?

a) 0.001
b) 0.01
c) 0.1
d) 0.0001

Answer 1

Mr. Cohen has a 0.001 probability of winning the prize in a state lottery where he must match a specific three-digit number, given that there are 1000 possible number combinations.

Step-by-step explanation:

Let's find the probability that Mr. Cohen's lucky number 247 will be selected in the state lottery.

For any given draw, the outcome must be a specific three-digit number. Since the digits 0 to 9 are available for each of the three places, there are a total of 10 x 10 x 10 = 1000 possible three-digit combinations.

To win a prize, the lottery number drawn must exactly match the number 247. There is only one such combination, so the probability of winning is given by the ratio of the number of winning outcomes to the total number of possible outcomes:

Probability of winning = Number of winning combinations / Total number of combinations = 1 / 1000 = 0.001.

Therefore, the correct answer to the probability that Mr. Cohen will win a prize is (a) 0.001.