Answer:
2.96% probability that Jason wins all 3 prizes.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the order in which the tickets are sorted is not important, and the fact that the tickets are thrown away means that there is no replacement. So we use the combinations formula to solve this question.
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:
3 tickets sorted from Jason's 10. So
[tex]D = C_{10,3} = \frac{10!}{3!(10-3)!} = 120[/tex]
Total outcomes:
3 tickets sorted from a set of 30. So
[tex]T = C_{30,3} = \frac{30!}{3!(30-3)!} = 4060[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{120}{4060} = 0.0296[/tex]
2.96% probability that Jason wins all 3 prizes.
