Question

1. A single card is drawn from a standard 52-card deck. What is the probability that the card is either a. A king, or a four, or a five b. A diamond, or a heart, or club c. A two, or a three, or a club d. A six, or a seven, or a spade, or a diamond Super D is a major video distributor that purchases blank DVDs from two sources: Disk Makers, which provides 62% of the DVDs, and Media Supply, which provides the remaining 38%. Historically, 3% of the DVDs Super D has purchased from Disk Makers have been defective, whereas 2% of the DVDs purchased from Media Supply have been defective. A randomly selected DVD is found to be defec- tive. Use Bayes' Theorem to determine the probability that the DVD came from Disk Makers.

Answer 1

aloil2020 Page 1 Ans: (2) Here, n(s) = 52. d There are 4 king or cu four e four five or so tatal 19 of getting a king, or a four orative cet E= Event nCE) = 12 : PLE). LE = Pce) (6) Here n(s) = 52. There are 13 13 heart on 13 club. diamond, b races sto total 39 et () - Event of getting diamond.or heat or club nCE) = 39 Ple) nie) . PLE) nis)

page-2 I (c) Here, n(s) = 52. There are 13 club Cards including 2,3 & there are 3 more 2 cards & 3 more 3 cards so tatal 19 cards let E- Event of getting 2,3 or club. . N(E) = 19 :: ple) - NLED 49 nes) Cards (d) Here There are including So tatal n (s) = 52. 13 spade cards, 13 diamond 6,7 & 2 more 6&7. Cards. 30 cards 6,7, spade or diamond let E= Event of getting .. PLE).mcreate PLE) = 18

Page 3 2 Ans: the following events: purchasing DVDs let us define Event DM is denoted as from Disk markers and Ms as purchasing Disi from media Supply. Event D as the purchased bro is defective. The values for the probabilities are listed below. The probability that the Dud is purchased from Disk makers is P (DM) = 0.62. The probability that the DVD is purchased from media suppliers is P(Ms) = 0.38 The probability that the DVD is defective given that it is purchased from Disk makers is P(0/PM) = 0.03 and the DVD is defective given that it is purchased from media supply is p(o/Ms) = 0.02.

page 4 using Baye's theorem we are calculating the value for promo) which is shown below. PLOMID). PCDM) x P(0/DM) mi plom) x P Olom)+PCMS),x PC oms) uz iba 0.62x0.03 0.62X0.03.+ 0.38X0.02 resto 0.0186 0.0186 +0.00te 36 +0.0076 0.0186 nos ( 0.0262 goue wilon P(OMD) = 0.7099