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**math951** An insurance agent offers his clients auto insurance, homeowner insurance, and renters insurance.

The purchase of homeowners insurance and renters insurance are mutually exclusive. The profile of agent's clients is as follows:

A= auto, B= homeowner, C= renter

i) 17 percent of these clients have none of these three products. -----> P(AuBuC)'= 17%

ii) 64 percent of clients have auto insurance -----------> P(A)=64 %

iii) Twice as many of the clients have homeowners insurance as have renters insurance -------------> P(C)= 2P(B)

iv) 35 percent of the clients have two of these products. -----------------> I am stuck on this one. I am thinking, P(A intersect B) + P(A intersect C) + P(B intersect C) = .35?

v) 11 percent of the clients have homeowners insurance, but not auto insurance. ------------------> P(B intersect A')

calculate percentage of clients who both have auto and renters insurance.