Question

Please provide detailed solutions for #13 and #15! Thank you.

13) In the town of Maplewood a certain type of DVD player is sold at just two stores, 43% of the sales 13) are from store A and 57% of the sales are from store B. 2.4% of the DVD players sold at store A are defective while 4.0% of the DVD players sold at store B are defective. If Kate receives one of these DVD players as a gift and finds that it is defective, what is the probability that it came from store A? A) 0.312 B) 0.453 C) 0.688 D) 0.024

Answer 1

Solution-13: P(StoreA) 0.43 P(StoreB)0.57 P(Defective | StoreA) 0.024 P(Defective | StoreB) 0.04 Given that the DVD player is defective, probability that it came from Store A: P(StoreA | Defective) From Baye's theorem P(StoreA) x P(Defectivel StoreA) P(StoreA) x P(Defectivel StoreA) P(StoreB) x P (Defectivel StoreB) P(StoreA | Defective) - P(StoreA | Defective) - P(StoreA | Defective) 0.3116 0.43 x 0.024 0.43 x 0.024 0.57 x 0.04 Solution-15: Probability of a risky investment will end up in total loss Sample size n!5 p 36% 0.36 Probability that at least one of the five investments will end up in total loss P(x 2 1) Using Binomial distribution: P(x 0) f(0) Co x (0.36)°x (1- 0.36)50.1074 Hence, P(x 1) 1- P(x 0) 1 0.1074 0.8926 Therefore, probability that at least one of the five investments will end up in total loss 0.8926