Question

each of the numbers from 1 through 30 is written on a table tennis ball and placed in a wire cage. each of th enumbers 20 through 45 is written
on a table tennis ball and placed in a diffrent wire cage. one ball is chosen at random form each spinning cage. which of the following describe:
P (The number is equal)

Can you explain how the answer is 11/780?
I got the answer 121/780, because 11 of the digits in each case are equal (20-30).

Would it not be 11/30 * 11/26?

How is the answer 11/780?

Answer 1

The probability of drawing of drawing one of the numbers that is common to both sets of balls is 11/N(A) where N(A) is the number of balls in one of the cages. Having drawn one of the common numbers the probability of drawing the same number from the other cage is 1/N(B).
Therefore the probability of the same number is
\[\frac{11}{N(A)\times N(B)}=\frac{11}{30\times 26}\]