3 The following data are available on three television factories that produce all the televisions used in a country. Factory A B % of total production 0.35 0.40 0.25 Probability of defect (Def 0.020 0.015 0.010 A television is selected at random and found to have a defect (Def). (i) Identify which one of the following expressions gives the required expression to correctly calculate the probability that the selected television was made in factory B. A1 P(made in B Def) * P(Def) P(made in A Def)P(Def)+ P(made in B|Def)P(Def) + P(made in C| Def)P(Def) A2 P(Defmade in B) P(made in B) P(Def made in A)P(made in A) + P(Def made in B)P(made in B) + P(Defmade in C)P(made in C) A3 P(Def|made in B) + P(made in B) [P(Def made in A) + P(made in A)] * [P(Defmade in B) + P(made in B)] [P(Defmade in C) + P(made in C)] A4 P(Defmade in B) P(Def made in A) + P(Defmade in B) + P(Def made in C) [2] (ii) Calculate, by using your answer to part (1), the probability that the selected television was produced by Manufacturer B. [2] [Total 4] 3 The following data are available on three television factories that produce all the televisions used in a country. Factory A B % of total production 0.35 0.40 0.25 Probability of defect (Def 0.020 0.015 0.010 A television is selected at random and found to have a defect (Def). (i) Identify which one of the following expressions gives the required expression to correctly calculate the probability that the selected television was made in factory B. A1 P(made in B Def) * P(Def) P(made in A Def)P(Def)+ P(made in B|Def)P(Def) + P(made in C| Def)P(Def) A2 P(Defmade in B) P(made in B) P(Def made in A)P(made in A) + P(Def made in B)P(made in B) + P(Defmade in C)P(made in C) A3 P(Def|made in B) + P(made in B) [P(Def made in A) + P(made in A)] * [P(Defmade in B) + P(made in B)] [P(Defmade in C) + P(made in C)] A4 P(Defmade in B) P(Def made in A) + P(Defmade in B) + P(Def made in C) [2] (ii) Calculate, by using your answer to part (1), the probability that the selected television was produced by Manufacturer B. [2] [Total 4]