The game called Lotto sponsored by the Louisiana Lottery Commission pays its lar

Question

The game called Lotto sponsored by the Louisiana Lottery Commission pays its largest prize when a contestant matches all 5 of the 39 possible numbers. Assume there are 39 ping-pong balls each with a single number between 1 and 39. 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 575,757. What is this in terms of probability? (Round your answer to 8 decimal places.) 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 39 numbers into two groups, winning numbers and nonwinning numbers. (Round your answer to 8 decimal places.) Probability c. Find the probability, again using the hypergeometric formula, for matching 3 of the 5 winning numbers. (Round your answer to 8 decimal places.) Probability d. Find the probability of matching 4 of the 5 winning numbers. (Round your answer to 8 decimal places.) Probability

Explanation / Answer

a)

Probability = 1 /575757 = 0.00000174

b)

Probability = 5C5 * 34C0 / 39C5 = 0.00000174

c)

Probability = 5C3 * 34C2 / 39C5 = 0.009744

d)

Probability = 5C4 * 34C1 / 39C5 = 0.000295

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