Question

A bag contains 9 balls numbered 1 to 9. Two balls are drawn at random. Find the probability that one is odd and the other is even.

Answer 1

Solution. Using formula for classical probability

$$p(A)=\frac {f}{N}$$

where A is event from a bag contains 9 balls numbered 1 to 9 two balls are drawn at random  that one is odd and the other is even; f is the frequency, or number of possible times the event could happen; N is the number of times the event could happen.

The number of combinations of the ability to select two balls out of 9 is equal to

$$N=\binom{9}{2}=\frac {9!}{7!2!}=36$$

From one to nine five odd numbers and four even. Therefore

$$f=\binom{5}{1}\binom{4}{1}=\frac {5!}{4!1!}\frac {4!}{3!1!} =5\times 4=20$$

As result get

$$p(A)=\frac {20}{36}=\frac{5}{9}$$

Answer.

$$\frac{5}{9}$$