Question

One asked to say a two digit no what is the probability of both been different

Answer 1

It would be easier first to find the probability of finding a two digit number which is a perfect square.

There are (99–10)+1 positive two digit numbers.

The largest two digit perfect square is 81 (9 squared) and the smallest is 16 (4 squared)

Then the numbers which meet this criteria are:

4,5,6,7,8,9. There are a total of 90 positive two digit numbers, so if we take the probability as the relative frequency, then we get  690=115 .

Now, since these events are disjoint, then the probability of not getting a perfect square is:

P=1−115=1415=0.933