The game called Lotto sponsored by the Louisiana Lottery Commission pays its largest prize when a contestant matches all 6 of the 40 possible numbers. Assume there are 40 ping-pong balls each with a single number between 1 and 40. Any number appears only once, and the winning balls are selected without replacement.
a. The commission reports that the probability of matching all the numbers are 1 in
3,838,380. What is this in terms of probability?
b. Use the hypergeometric formula to find this probability.
The lottery commission also pays if a contestant matches four or five of the six winning numbers.
c. Find the probability, again using the hypergeometric formula, for matching 4 of the 6 winning numbers.
d. Find the probability of matching 5 of the 6 winning numbers.