Question

Many states have a lottery game, usually called Pick-4, in which you pick a 4-digit number (for instance, 3129). During the lottery drawing, there are four bins each containing balls labeled 0 through 9. One ball is drawn at random from each bin to select the winning lottery number

. a. If you buy one ticket with one 4-digit number, what is the probability that you will win this game?

b. What is the probability that the 4-digit number drawn has exactly two of the four digits the same (for instance, 1223, 9095, or 1701)?

Answer 1

The number of combination of 4-digit number in the total number is 10

$\binom{10}{1}\binom{10}{1}\binom{10}{1}\binom{10}{1}=10000$

a. the probability that you will win this game that is only one ticket is winning

$p(win)=\frac{1}{10000}$

b. the probability that the 4-digit number drawn has exactly two of the four digits the same is

$p(2)=\frac{\binom{4}{2}}{10000}=\frac{6}{10000}=0.0006$