Answer:
[tex]\frac{1}{23751}[/tex] probability that you will win
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order is not important, so we use the combinations formula to solve this problem.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
the 4 number chosen are the 4 correct. So
[tex]D = C_{4,4} = \frac{4!}{4!(4-4)!} = 1[/tex]
Total outcomes:
4 numers from a set of 29. So
[tex]D = C_{29,4} = \frac{29!}{4!(29-4)!} = 23751[/tex]
Probability
[tex]P = \frac{D}{T} = \frac{1}{23751}[/tex]
[tex]\frac{1}{23751}[/tex] probability that you will win
