# Math Help - Probability of number begins with zero (0000-9999)

1. ## Probability of number begins with zero (0000-9999)

a four digit numbers, in range of 000-9999, is formed. Find the probability of the numbers begins and end with zero.

the ans is 19/100. how to do this?

find the probablity of the numbers contains ecxactly two non-zero digits. the ans is 243/5000 . how to do this?

2. ## Re: Probability of number begins with zero (0000-9999)

why don't you put some effort into it for once and try and figure it out on your own.

3. ## Re: Probability of number begins with zero (0000-9999)

I did try. But I cant get the ans. Otherwise I wouldnt ask it here.

4. ## Re: Probability of number begins with zero (0000-9999)

Originally Posted by delso
I did try. But I cant get the ans. Otherwise I wouldnt ask it here.
show us what you did. You ask an awful lot of questions w/o seeming to put any effort into them first.

5. ## Re: Probability of number begins with zero (0000-9999)

Originally Posted by delso
a four digit numbers, in range of 000-9999, is formed. Find the probability of the numbers begins and end with zero.
the ans is 19/100. how to do this?

find the probablity of the numbers contains ecxactly two non-zero digits. the ans is 243/5000 . how to do this?
Do you mean 0000-9999 range?

If so:
19/100 is not correct...check your problem!

243/5000 is correct.

The "how to" is your teacher's responsibility, not ours.

6. ## Re: Probability of number begins with zero (0000-9999)

Originally Posted by Wilmer
Do you mean 0000-9999 range?

If so:
19/100 is not correct...check your problem!

243/5000 is correct.

The "how to" is your teacher's responsibility, not ours.
If you set the first and last digits to 0, how many digits are left free to set?
Spoiler:
2

How many different ways can each digit be set?
Spoiler:
10

So how many ways can 2 digits be set?
Spoiler:
$10^2=100$

How many possible 4 digit numbers are there total?
Spoiler:
$10^4=10000$

So what is the probability of a 4 digit number with the first and last digits equal to 0?
Spoiler:
$\dfrac{100}{10000}=\dfrac 1 {100}$

Another way of looking at it

How many ways can you set 2 digits with 10 numbers.
Spoiler:
$10^2=100$

You are selecting a single pattern of 2 digits for the 1st and 4th slots. This is 1 out of the number above.

So the probability is
Spoiler:
$\dfrac 1 {100}$