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 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 a. The commission reports that the probability of matching all the numbers are 1 in 201,376. 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 mission 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 numbe decimal places.) rs. (Round your answer to 8 Probability 0.00000497 Find the probability, again using the hypergeometric formula, for matching 3 of the 5 winning numbers. Round your answer to 8 decimal places.) c. Probability 0.01743008 d. Find the probability of matching 4 of the 5 winning numbers. (Round your answer to 8 decimal places.) Probability

Explanation / Answer

a)

It is

P(win) = 1/201376 = 0.00000497 [ANSWER]
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B)

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    32      
K = number of successes in the population =    5      
n = sample size =    5      
x = number of successes in the sample =    5      
          
Thus,          
          
P(   5   ) =    0.00000497 [ANSWER]

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C)

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    32      
K = number of successes in the population =    5      
n = sample size =    5      
x = number of successes in the sample =    3      
          
Thus,          
          
P(   3   ) =    0.01743008 [answer]

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d)

Note that the probability of x successes out of n trials is          
          
P(x) = C(N-K, n-x) C(K, x) / C(N, n)          
          
where          
N = population size =    32      
K = number of successes in the population =    5      
n = sample size =    5      
x = number of successes in the sample =    4      
          
Thus,          
          
P(   4   ) =    0.000670389 [ANSWER]

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