Question

A person must select 4 numbers from 16 numbers for a single ticket in a lottery game. Only one number has to match in order to win a prize. Find the probability of winning if a person buys one ticket. (Note: The numbers can be selected in any order.) Round to four decimal places, if necessary.

Answer 1

Let event A = Not matching a single number. Then P(A) = 3/4*12/15*12/14*12/13 = 0.4747252747...
Thus, the probability of matching at least one number, A(bar), equals 1 - P(A) = 0.5252747253.

Answer 2

This can be regarded as sampling without replacement. The probability of having no matching numbers is:
\[P(0\ matches)=\frac{4C0\times12C4}{16C4}=0.27198\]
So the probability of having at least one matching number is:
1.00000 - 0.27198 = 0.728