SOLUTION: A.) Grand prize for a lottery is choosing 6 numbers correctly out of 47 (order does not matter). What is the probability of winning this lottery? B.) If you choose 6 numbers ou

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Question 1178541: A.) Grand prize for a lottery is choosing 6 numbers correctly out of 47 (order does not matter). What is the probability of winning this lottery?
B.) If you choose 6 numbers out of 47 and 5 are chosen correctly you win second prize. What is this probability?
Explain.
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
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A.) Grand prize for a lottery is choosing 6 numbers correctly out of 47 (order does not matter). What is the probability of winning this lottery?
B.) If you choose 6 numbers out of 47 and 5 are chosen correctly you win second prize. What is this probability?
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(A)  The winning first prize is choosing a subset of 6 numbers correctly from the set of 47 numbers, without looking the order.

          P = 1%2FC%5B47%5D%5E6 = 1%2F10737573 = 9.31309E-08.         ANSWER



(B)  To win the second prize, there are  C%5B6%5D%5E5%2A%2847-6%29 = 6*41  favorable sets of 6 numbers

     (indeed, from winning 6 numbers, we can form  C%5B6%5D%5E5 = 6 subsets of 5 good numbers and then add 
      to each of these subsets of 5 good numbers any of remaining  41  BAD numbers).


     So, the probability to win the second prize is then


         P = favorable%2Ftotal = %286%2A41%29%2FC%5B47%5D%5E6 = %286%2A41%29%2F10737573 = 2.29102E-05.     ANSWER

Solved.