# Math Help - Probability question.

1. ## Probability question.

Hi All,

I have a question related to probability :-

Q - Ten tickets are numbered 1,2,3 ..... 10 .Six tickets are selected at random one at a time with replacement.The probablity that the largest number appearing on the selected ticket is 7 is :-

Sol - As per my understanding, I tried solving the above question in the way mentioned below:-

Six tickets can be drawn in the 10.10.10.10.10.10
Sample space for above question is n(s) = 10 ^6

As the largest number appearing on the selected ticket is 7.
So out of the selected 6 tickets one must be 7 and rest 5 were either equal to or less than 7. These can drawn in 7.7.7.7.7 = 7^5.

Hence n(e) = 7^5

Therefore the probability p(e) = n(e)/n(s) = (7^5)/(10^6)
-----------------------------------------------------------

But the book Answer is - (7^6 - 6^6)/10^6.

Any help would be greatly appreciated.

Thanks,
Ashish

2. Originally Posted by a69356
Hi All,

I have a question related to probability :-

Q - Ten tickets are numbered 1,2,3 ..... 10 .Six tickets are selected at random one at a time with replacement.The probablity that the largest number appearing on the selected ticket is 7 is :-

Sol - As per my understanding, I tried solving the above question in the way mentioned below:-

Six tickets can be drawn in the 10.10.10.10.10.10
Sample space for above question is n(s) = 10 ^6

As the largest number appearing on the selected ticket is 7.
So out of the selected 6 tickets one must be 7 and rest 5 were either equal to or less than 7. These can drawn in 7.7.7.7.7 = 7^5.

Hence n(e) = 7^5

Therefore the probability p(e) = n(e)/n(s) = (7^5)/(10^6)
-----------------------------------------------------------

But the book Answer is - (7^6 - 6^6)/10^6.

Any help would be greatly appreciated.

Thanks,
Ashish
The numerator is the number of ways of choosing seven numbers that are no larger than 7 subject to the restriction that at least one of the numbers is 7.

This is equal to choosing the seven numbers from the numbers 1 - 7 minus choosing the 7 numbers from the numbers 1 - 6. You you have to subtract the latter term so that you don't have choices like 6, 5, 6, 3, 2, 1 etc.

So the numerator will be $7^6 - 6^6$.

3. Thanks a lot for the quick reply. Can we take an example for the above question? It would be of great help!!!

Thanks,
Ashish