Question

A producer of a certain type of electronic component ships to suppliers in lots of twenty. Suppose that 60% of all such lots contain no defective components, 30% contain one defective component, and 10% contain two defective components. A lot is picked, two components from the lot are randomly selected and tested, and neither is defective.

(a) What is the probability that zero defective components exist in the lot?

(b) What is the probability that one defective exists in the lot?

(c) What is the probability that two defectives exist in the lot?

Answer 1

288katio) Guven produces of a certain type of Electronic component Sbias to Suppliers in lots of twenty let PCD.) = 0.60 PCD): 0.30 Plog): 0.10 (no defective) Cone defective) ctwo defecture). and neither is defective. a non defective item in Let Ebe the o componente de picked yf item is no defective, we can select 200g ways . PCAID.) Local select a non defective items in by gf gitem is defective, we can qet '60 31960 ways P(A1D): 19 .11.09 1 a son defective items in st & items is die fective, we can select 16gx co = 180g ways,.. . 193 P(410g) = e nteret 190 : 0.8033 0.8053 Q the poobability thay yeso defective components Saists in the lol is

P(AIDS) PCDO) PODOLA) : PCADO) PCDO) + P(AID) PCD)+ PLAID) PCD) 1 X 0.60 (1x D-60)+ (y-4 x 3) +(o-8053 xo:)) 0.60 0.6+ 0.27+ 0-08053 - 0.6 0.95053 0.6312 The probability P (Dila) that one defective Bxis in the lot is P(A1D) PODI) PEAID) POD) + P(AIDI) PCD1)+ P(A/D3) P(D2) 0.980.3 (1X0.6) + (0.9%0.3) + (0.8053x0.1) : 0.97 0.95053 : 0 2841 • The probability that two de fertives Saist in the lot is PC Dola) PCAID.) PCD) PCA)DO) PIDO) + ACAID) PCD)) + PEAID) PCD) El 018053x0.1 TIX06) + (0.9x0-3) +(0-805380.1) 0.08053 0.95053 0.0847,