# Probability question

• Sep 21st 2013, 08:11 AM
alexander9408
Probability question
A box contains 10 digits in it, which is 0,1,2,3,4,5,6,7,8,9. When a digit is drawn out, a replacement is placed into the box. A 3-digit number is drawn.
1. The probability of all the drawn digit are the same.
2. The probability of two same digits is drawn.
3. The probability of all the digits drawn are different.
• Sep 21st 2013, 08:37 AM
Plato
Re: Probability question
Quote:

Originally Posted by alexander9408
A box contains 10 digits in it, which is 0,1,2,3,4,5,6,7,8,9. When a digit is drawn out, a replacement is placed into the box. A 3-digit number is drawn.
1. The probability of all the drawn digit are the same.
2. The probability of two same digits is drawn.
3. The probability of all the digits drawn are different.

There are $\displaystyle 10^3$ possible numbers: $\displaystyle 000,~001\text{ to }998,~999$.

1. How many of those have all digits the same? Now divide.

2. How many of those have two digits the same? Now divide.

• Sep 21st 2013, 08:54 AM
alexander9408
Re: Probability question
1. 10/1000=0.01
2. How can I get the numbers with 2 same digit? Did I needs to list out all the numbers from 000 to 999 and picks the numbers that have 2 same digit?
• Sep 21st 2013, 09:09 AM
Plato
Re: Probability question
Quote:

Originally Posted by alexander9408
1. 10/1000=0.01
2. How can I get the numbers with 2 same digit? Did I needs to list out all the numbers from 000 to 999 and picks the numbers that have 2 same digit?

There are ten ways to select the doubled digit; nine ways to select the single digit; three ways to arrange those digits.