The game called Lotto sponsored by the Louisiana Lottery Commission pays its largest prize when a contestant matches all 3 of the 25 possible numbers. Assume there are 25 ping-pong balls each with a single number between 1 and 25. 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 2,300. What is this in terms of probability? (Round your answer to 8 decimal places.)

  

b.

Use the hypergeometric formula to find the probability of matching all 3 winning numbers. The lottery commission also pays if a contestant matches 1 or 2 of the 3 winning numbers. Hint: Divide the 25 numbers into two groups, winning numbers and nonwinning numbers. (Round your answer to 8 decimal places.)

 

c.

Find the probability, again using the hypergeometric formula, for matching 1 of the 3 winning numbers. (Round your answer to 8 decimal places.)

 

d.

Find the probability of matching 2 of the 3 winning numbers. (Round your answer to 8 decimal places.)

 

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