Let M be the maximum value of the product of two positive integers when their sum is 66 . Let the sample space S = x ∈ Z : x ( 66 - x ) ≥ 5 9 M and the event A = x ∈ S : x is a multiple of 3 . Then P ( A ) is equal to

Step-by-step solution

Given, Sum of two integer is 66 , so one number will be x and other will be 66 - x , And given M is maximum value of their product, So let y = x 66 - x ⇒ y = 66 x - x 2 Now differentiating to find maxima and minima we get, d y d x = 66 - 2 x Now equating with zero to find point of maxima as y = 66 x - x 2 represents a downward parabola so it will give maxima, So d y d x = 0 ⇒ 66 - 2 x = 0 ⇒ x = 33 , Hence, the value of M = 33 × 33 = 1089 Now solving x 66 - x ≥ 5 M 9 ⇒ x 66 - x &#8