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Suppose we want to pick two numbers  from {1,2……,100} randomly . The probability that sum of the two numbers is divisible by 5 is _________________

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Suppose we want to pick two numbers  from {1,2……,100} randomly . 

// means that we have to select two numbers at one go and there is no point for replacement...

 sum of the two numbers is divisible by 5.

// from the set of 100 we need to select 2 numbers {{5,10}{1,9}{6,9}..........}}

20 modulo 5≡0 are 20...........@1

20 modulo 5≡1 are 20..........@2

20 modulo 5≡2 are 20...........@3

20 modulo 5≡3 are 20............@4

20 modulo 5=4 are 20............@5

=select any two numbers from @1 or select one number from @2 and other from set @5  or one from @3 and other from @4 

  = (20C2 + 20C1 *20C1 + 20C1 *20C1) = 990 ways

sample space = selecting 2 numbers from 100 numbers in 100C2.

probability = 990/ 100C2 = 990/50*99=1/5 = 0.2 answer .

                                                           

 

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