Question

Ten balls numbered 0, 1, 2, ….., 9 are put in a box and two balls are taken at random. What is the probability that both numbers are odd

Answer 1

Notice that there 5 odd numbers among 0,1,..,9:
they are:
1,3,5,7,9

The probability to take the first odd number is
5/10 =
0.5

If we take an odd number, then it remains 9 numbers among which we
have 4 odd numbers.
Hence the probability to take an odd number in this case
is
4/9.

Therefore the probability of taking both odd numbers
is

p = 5/10 * 4/9
= 1/2 * 4/9
= 2/9