# probability

• Jan 7th 2009, 04:23 PM
asugirl87
probability
What is the probability that a 6-digit phone number contains at least one 2? (Repetition of numbers and lead zero are allowed).
• Jan 7th 2009, 04:38 PM
Mush
Imagine the situation as being a room with 6 phones. Each phone has 10 digits on it, and you have to pick one digit from each phone!

As such there are 10 different ways you can choose 1 from 10. And you have to choose 6 of these. Hence there are \$\displaystyle 10^6\$ combinations!

Now lets consider the same situation, only now all the 2s on the phones have been removed. So now there are 6 phones, each with only 9 digits, (0,1,3,4,5,6,7,8,9). So you are choosing 1 button from 9, 6 times! Hence \$\displaystyle 9^6\$.

So we have concluded that there are \$\displaystyle 10^6 \$ combinations, and \$\displaystyle 9^6 \$ of them have no 2!

Hence the probability that there is at least one 2 is :

\$\displaystyle 10^6 - 9^6 = 468559\$
• Jan 29th 2009, 07:39 AM
ramvenk
The response is attached as a gif image, hope this helps you.