The game called lotto sponsored by the Louisiana Lottery Commission pays its largest prize when a contestant matches all 5 of the 32 possible numbers. Assume there are 32 ping-pong balls each with a single number between 1 and 32. Any number appears only once, and the winning balls are selected without replacement. Round all answers to 8 decimal places.
a. The commission reports that the probability of matching all the numbers are 1 in 201,376. What is this in terms of probability?
b. Use the hypergeometric formula to find the probability of matching all 5 winning numbers. The lottery commission also pays if a contestant matches 3 or 4 of the 5 winning numbers. Hint: Divide the 32 numbers into two groups, winning numbers, and nonwinning numbers.
c. Find the probability, again using the hypergeometric formula, for matching 3 of the 5 winning numbers.
d. Find the probability of matching 4 of the 5 winning numbers.