exercise:Faabf07189

A company offers a basic life insurance policy to its employees, as well as a supplemental life insurance policy. To purchase the supplemental policy, an employee must first purchase the basic policy. Let [math]X[/math] denote the proportion of employees who purchase the basic policy, and [math]Y[/math] the proportion of employees who purchase the supplemental policy. Let [math]X[/math] and [math]Y[/math] have the joint density function [math]f(x,y) = 2(x+y)[/math] on the region where the density is positive.

Given that 10% of the employees buy the basic policy, calculate the probability that fewer than 5% buy the supplemental policy.

• 0.010
• 0.013
• 0.108
• 0.417
• 0.500

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