The lottery draws 100 tickets, among which 10 are winning. The student bought 2 tickets.

The lottery draws 100 tickets, among which 10 are winning. The student bought 2 tickets. What is the probability that he won nothing?

The total number of outcomes when choosing two tickets:
C (100.2) = 100! / (2! 98!) = 99 100/2 = 4950.
Number of ways to take 2 non-winning tickets out of 90:
C (90.2) = 90! / (2! 88!) = 89 90/2 = 4005.
Number of ways not to choose any winning ticket out of 10:
C (10.0) = 1.
Probability that the student won nothing:
P (0) = C (10.0) C (90.2) / C (100.2) = 14005/4950 = 0.809.
Answer: The probability that the student won nothing is 0.809.