In ''The Numbers Game,'' a state lottery, four numbers are drawn with replacement from an urn containing the digits 0-9, inclusive. Find the probability of a ticket holder having the indicated winning ticket.



All four digits in any order(including the other winning tickets)

To find the probability of winning the lottery with all four digits in any order, we need to determine how many possible combinations of numbers there are and how many of them would be winning tickets.

There are a total of 10 digits (0-9) that can be chosen for each of the four positions on the ticket. Since the digits are chosen with replacement, it means that the same digit can be chosen more than once.

The number of total possible combinations of digits is calculated by multiplying the number of choices for each position. In this case, it is 10 choices for each of the four positions, so the total number of combinations is 10^4 = 10,000.

Now, let's find out how many of those combinations would be considered winning tickets. Since the order of the digits does not matter, we can think of it as selecting four digits from the pool of 10.

The number of ways to select four digits out of 10 without considering the order is given by the combination formula: C(10,4) = 10! / (4!(10-4)!) = 210.

Therefore, there are 210 possible winning combinations out of the total 10,000 combinations.

To find the probability of having the indicated winning ticket, we divide the number of winning combinations by the total number of possible combinations:

Probability = Number of winning combinations / Total number of combinations = 210 / 10,000 = 0.021 = 2.1%.

1/10 *1/10 * 1/10 * 1/10 = 1/10,000