Question

In the Numbers Game, a state lottery, four numbers are drawn with replacement from an urn containing balls numbered 0-9, inclusive. Find the probability that a ticket holder has the indicated winning ticket.
The first two digits in exact order.

Answer 1

There are 10 digits from 0 to 9, inclusive.

Thus, number of ways in which four numbers will be drawn from an urn containing balls numbered 0-9, inclusive is given by $10^4=10,000$

The number of ways in which a ticket holder will have the first two digits in the correct order is the same as the number of ways in which two numbers will be drawn from the urn containing balls numbered 0-9, inclusive and is given by $10^2=100$

Therefore, the probability that a ticket holder has the first two digits in exact order is given by $\frac{100}{10,000} = \frac{1}{100} =0.01$