Let x+y=20,x,y∈W, the set of non-negative integers. If S is the maximum value of xy and the probability of xy not less than 3S4 is nm, where m and n are co-prime, then the value of n+m is
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Solution
Given x+y=20 The maximum value of xy is when x=y=10, S=10×10=100⇒3S4=75
Now, xy≥75 ⇒x(20−x)≥75⇒20x−x2≥75⇒x2−20x+75≤0⇒(x−5)(x−15)≤0⇒x∈[5,15] Required number of values of x is 11 Total number of possible values of x is 20 Therefore, the required probability =1120 ⇒nm=1120⇒n+m=31