Name: Date: Chapter 7.5 - 7.7 Distributions Take-Home 5. (15 points) A factory has two machines, A and B. The number of breakdowns of each machine is independent from day to day. Let A be the number of breakdowns of Machine A on any given day. The probability distribution for A can be modelled by the following table. a 0 2 3 P(A = a) 0.55 0.3 0.1 0. 5 5 +0. 3 to. Ith = 1 a. Find k. 15 = 0.05 [2 marks] ib. (1) A day is chosen at random. Write down the probability that [3 marks] Machine A has no breakdowns. 10.55 ) (ii) Five days are chosen at random. Find the probability that Machine A has no breakdowns on exactly four of these days. P ( x = 4 ) = 0. 2058-70. 206 Let B be the number of breakdowns of Machine B on any given day. The probability distribution for B can be modelled by the following table. b 0 3 P(B = 6) 0.7 0.2 0.08 0.02 ic. Find E(B). E ( B ) = 0.2 + ( 2 x0,08 ) + ( 3 *0.02 ) [2 marks] E (3 = 0. 42 On Tuesday, the factory uses both Machine A and Machine B. The variables A and B are independent. (o. | xo. 7) +( 0 .5 5 xo. 8 ) +( 0. 3 x 0. 2) = = 16.174) id. (i) Find the probability that there are exactly two breakdowns on [8 marks] Tuesday. (0. | 740 (ii) Given that there are exactly two breakdowns on Tuesday, find the probability that both breakdowns are of Machine A. 0, 1 X 0 . 7 0. 174 = 0.4022 10 . 02