Question

In New York State’s numbers game, an individual chooses a 3 digit number to play the game. This 3 digit number can range from 000 to 999 inclusive. What is the probability that a person will win the game if he/she selects: DO NOT REDUCE

1. a) The 3 digit number 217?
2. b) A 3 digit number where the digits 4,2,7 appear in any order?
3. c) All 3 digit numbers beginning and ending with a 7?

Answer 1

a) The probability that he wins if there is a 3 digit number 217 selected is computed as:
= 1/10³ = 0.001
Therefore 0.001 is the required probability here.

b) Total numbers with 4, 2, 7 in any order = 3! = 6
Therefore the required probability is computed here as:
= 6/1000 = 0.006
Therefore 0.006 is the required probability.

c) Total numbers beginning as well as ending with 7 is computed here as:
7 _ 7
There are 10 ways to fill the middle digit here.
Therefore the probability here is computed as:
= 10/1000 = 0.01
Therefore 0.01 is the required probability here.