Question

A number between 5 and 10 is picked at random. What is the probability that the number picked is odd?

Answer 1

Ok so
probablity is $\frac{desired\ outcomes}{total\possible\ outcomes}$

odd numbers between 5 and 10
7 and 9
desired outcomes is 2 since 2 numbers

total numbers between 5 and 10
4 because the numbers are 6,7,8,9


so
deired outcomes=2
toatl possible=4

probability=2/4=1/2
answer is 1/2

Answer 2

             Probability =
                                       (number of successful possibilities)
                           divided by
                                       (total number of all possibilities) .

When you say "between 5 and 10", I don't know whether
you mean to include 5 and 10.

If you do include 5 and 10:
             -- then there are 3 odd numbers  (5, 7, and 9)
             -- 6 total possibilities  (5, 6, 7, 8, 9, and 10)

               Probability = 3/6  =  0.5  =  50% .

If you don't include 5 and 10:
             -- then there are 2 odd numbers  (7 and 9)
             -- 4 total possibilities   (6, 7, 8, and 9)

               Probability =  2/4  =  0.5  =  50% .

Well will ya look at that !  It doesn't make any difference
whether you include 5 and 10 or you don't include them.
The probability of an odd number is  50%  either way !