A new car dealer offers three packages of optional equipment for a particular model. There is an automatic transmission package, with a profit of $200 to the dealer, an airconditioning package, with a profit of $150, and an interior décor package, with a profit of $100. Data indicate that 80% of customers order the automatic transmission package; 60% of customers who order the automatic transmission package, also order the airconditioning package. 50% of customers who do not order the automatic transmission package, order the air-conditioning package. Of customers who ordered both packages, 40% order the interior décor package. Of customers who ordered exactly one of the transmission and air-conditioning packages, 30% order the interior décor package. Of customers who order neither of the other packages, 20% order the interior décor package. Hint: you can think of probability trees in order to find the distribution for Y. Let Y=the number of packages ordered on a randomly chosen new car. Q12. Compute P(Y=2) a) 0.414 b) 0.080 c) 0.314 d) 0.48

Q13. Compute P(Y=0) a) 0.414 b) 0.080 c) 0.314 d) 0.48

Q14. Compute P(Y=3) a) 0.414 b) 0.080 c) 0.192 d) 0.48

Q15. Compute P(Y≥2) a) 0.5 b) 0.414 c) 0.606 d) 0.070