If everyone in your class writes down her favorite two-digit number.

Question

If everyone in your class writes down her favorite two-digit number, what is the probability that two people will have written down the same number? Note: assume that there are 4 students in your class.

Answer 1

Amina,

            The sample space is all the 2 number permutations  from 0 1 2 3 4 5 6 7 8 9 or 10!/8!=90 we count 12 and 21 as different because they are different numbers. The probability that any given two-digit number is chosen is 1/90 and since the additional choice is an independent event the probability that two people will have the same number is 3*(1/90)*(1/90) or 3/8,100. Since there are 3 ways to choose 2 out of 4.

 

Jim