# Question 06856

Jun 6, 2015

The probability to that both balls have odd numbers is $\frac{3}{10}$

There are 5 balls in the box A, numbered 1 2 3 4 5, and there are 4 balls in the box B, numbered 1 2 3 4.

You take one ball from box A and one ball from box B.
In other words, for every ball you take from box A, you take one ball from box B.
That gives you a total of $5 \cdot 4 = 20$ different possible combinations of "one ball from box A plus one ball from box B".

Among the five balls in the box A, three have an odd number and two have an even number.
Among the four balls in box B, two have an odd number and two have an even number.

Therefore, there is a total of $3 \cdot 2 = 6$ different possible combinations of "a ball with an odd number from box A plus a ball with an odd number from box B".

The probability of an event to happen is calculated as

(number of favorable outcomes)/(number of possible outcomes)

Here, that is $\frac{6}{20} = \frac{3}{10}$ (also note that 3/10 = 30%#)

And since a good picture is worth a thousand words: