Let's begin with a rather straightforward lottery in which players select four digits. The winning number is commonly selected in the following fashion: 10 Ping Pong balls (each with a digit 0 through 9 written on it) are placed in a hopper. One Ping Pong ball is selected. That digit now goes in the first place. That Ping Pong ball is put back in the hopper and the process is repeated three times.

Question

Let's begin with a rather straightforward lottery in which players select four digits.  The winning number is commonly selected in the following fashion:  10 Ping Pong balls (each with a digit 0 through 9 written on it) are placed in a hopper.  One Ping Pong ball is selected.  That digit now goes in the first place.  That Ping Pong ball is put back in the hopper and the process is repeated three times.

What is the probability of picking a winning number?

Then suppose the Ping Pong ball was not replaced.  Now what is the probability?

Reiny · Answer

10 cases for 1st draw, 10 for the 2nd, 10 for the third, 10 for the 4th prob = 1/10^4 = 1/10000 if ball is not returned prob = 1/(10*9*8*7) = 1/5040