# Answer to Question #12921 in Statistics and Probability for Naren

Question #12921

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

Expert's answer

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

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

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