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.

Please help me in figuring out the right way in solving the above question.

Any help would be greatly appreciated.

Thanks,
Ashish

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.

Please help me in figuring out the right way in solving the above question.

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 $\displaystyle 7^6 - 6^6$.

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

Thanks,
Ashish