The game called Lotto sponsored by the Louisiana Lottery Commission pays its largest prize when a contestant matches all 7 of the 38 possible numbers. Assume there are 38 ping pong balls each with a single number between 1 and 38. Any number appears only once, and the winning balls are selected without replacement.
a. The commission reports that the probability of matching all numbers are 1 in 12,620,256. What is this in terms of probability? round to 8 decimal places
b. Use the hypergeometric formula to find this probability. The lottery commission also pays if a contestant matches 5 or 6 or7 of the winning numbers. Hint: Divide the 38 numbers into 2 groups. Winning numbers and non-winning
numbers. Round to 8 decimal places.
c. Find the probability again using the hypergeometric formula for matching 5 of the 7 winning numbers. Round to 8 decimal places.
d. Find the probability of matching 6 of the 7 winning numbers. Round to 8 decimal places.