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 1178551: `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.
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
probability of first's being correct is (6/47), and this is multiplied by (5/46)(4/45)(3/44)(2/43)(1/42)
that value is 720/7,731,052,560
=9.13 X 10^(-8)
or 1 in 10,737,573
-
There are 6 ways to do this, and one way is
first number doesn't matter (probability 1)*(5/46)(4/45)(3/44)*(2/43)*1/42)=120/164,490,480.
But there are 6 ways this can occur, so the answer is 720/164,490,480
=4.38 x 10^(-6)
or 1 in 228,459
Answer by ikleyn(52858)   (Show Source): You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~ 


(A)  The winning first prize is choosing a subset of 6 numbers correctly from the set of 47 numbers, without looking the order.

          P =  =  = 9.31309E-08.         ANSWER



(B)  To win the second prize, there are   = 6*41  favorable sets of 6 numbers

     (indeed, from winning 6 numbers, we can form   = 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 =  =  =  = 2.29102E-05.     ANSWER

Solved.



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