The game called Lotto sponsored by the Louisiana Lottery Com

The game called Lotto sponsored by the Louisiana Lottery Commission pays its largest prize when a contestant matches all 4 of the 41 possible numbers. Assume there are 41 ping-pong balls each with a single number between 1 and 41. Any number appears only once, and the winning balls are selected without replacement.

The commission reports that the probability of matching all the numbers are 1 in 101,270. What is this in terms of probability? (Round your answer to 8 decimal places.)

Use the hypergeometric formula to find the probability of matching all 4 winning numbers. The lottery commission also pays if a contestant matches 2 or 3 of the 4 winning numbers. Hint: Divide the 41 numbers into two groups, winning numbers and nonwinning numbers. (Round your answer to 8 decimal places.)

Find the probability, again using the hypergeometric formula, for matching 2 of the 4 winning numbers. (Round your answer to 8 decimal places.)

Find the probability of matching 3 of the 4 winning numbers. (Round your answer to 8 decimal places.)

Solution