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Question

If p and q are chosen randomly from the set {1,2,3,4,5,6,7,8,9,10} with replacement, determine the probability that the roots of the equation x2+px+q=0are real.___


Solution

If roots ofx2+px+q=0 are real,
thenp24q0 .....................(1)
 Both p,q, belong to set S=1,2,310 when
p=1,      no value of q from S will satisfy (1)  
p = 2     q=1 will satisfy
p = 3     q=1,2
p = 4     q=1,2,3,4
p = 5    q=1,2,3,4,5,6
p = 6    q=1,2,3,4,5,6,7,8,9,
For p = 7,8,9,10 all the ten values of q will satisfy.
Sum of these selections is 
1+2+4+6+9+10+10+10+10=62
But the total number of selections of p and q without any order is 10×10=100
Hence the required probability is 
=62100=0.62

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