velue 5.00 points The game called Lotto sponsored by the Louisiana Lottery Commi

Question

velue 5.00 points The game called Lotto sponsored by the Louisiana Lottery Commission pays its largest prize when a single number between 1 and 35. Any number appears only once, and the winning balls are selected contestant matches all 6 of the 35 possible numbers. Assume there are 35 ping-pong without replacement a. The commission reports t balls each with a hecmiin sio the probhahily mating al ubarn are 1 in 1.623,160. s 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 6 winning numbers. The lottery commission also pays if a contestant matches 4 or 5 of the 6 winning numbers. Hint: Divide the 35 numbers into two g decimal places.) groups, winning numbers and nonwinning numbers. (Round your answer to 8 Probability c. Find the probability, again using the hypergeometric formula, for matching 4 of the 6 winning (Round your answer to 8 decimal places.) Probability d. Find the probability of matching 5 of the 6 winning numbers (Round your answer to 8 decimal places.) Probability Reterences eBook & Resources Worksheet

Explanation / Answer

a)

P = 1/1623160 = 0.000000616082 = 0.00000062 [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 =    35      
K = number of successes in the population =    6      
n = sample size =    6      
x = number of successes in the sample =    6      
          
Thus,          
          
P(   6   ) =    0.000000616082 [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 =    35      
K = number of successes in the population =    6      
n = sample size =    6      
x = number of successes in the sample =    4      
          
Thus,          
          
P(   4   ) =    0.003751941 [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 =    35      
K = number of successes in the population =    6      
n = sample size =    6      
x = number of successes in the sample =    5      
          
Thus,          
          
P(   5   ) =    0.000107198 [ANSWER]

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