In Sweden the lottery works on a 7 out of 35 basis That is y

In Sweden the lottery works on a 7 out of 35 basis. That is you purchase a lottery ticket and choose 7 numbers out of the numbers between 1 and 35. If you have less than four right numbers, you loose. What is the probability to loose? What is the probability to have all five numbers right?

Solution

1.

Note that P(less than x) = P(at most x-1)          
          
Using a cumulative hypergeometric distribution table or technology, matching          
          
where          
N = population size =    35      
K = number of successes in the population =    5      
n = sample size =    7      
x = critical number of successes in the sample =    4      
          
Thus,          
P(at most   3   ) =    0.996916509
          
Therefore,          
P(less than   4   ) =    0.996916509 [ANSWER]

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2.

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 =    5      
n = sample size =    7      
x = number of successes in the sample =    5      
          
Thus,          
          
P(   5   ) =    6.46886*10^-5 [ANSWER]