Cons der purchasing syster of audio companants consisting of a recer er, a pair

Question

Cons der purchasing syster of audio companants consisting of a recer er, a pair af speakers, and CD payer. Let Ai ba the event that the reco ver functions ropar y throughout the war an period 2 be the avent that the speakers unction properly throughout the warranty period, and A3 be the event that the ED player functions properly throughout the warranty period. Supposc that these events are (mutually)dedent with , 2.7, ad A) Rond your anwers to four decimal places) (a) What ltha probabl ity that all threa companants function propariy throughaut the warranty pariod? a tha probablility al (b) What is the probabiity that at least one component needs service during the waranty peried? anty period? c) What is the probabiity that all three components need service during the warranty perod? (d) What is the probabi ity that only the recciver needs servica during the warranty pariad? service (e) what is the probabi ity that cxactly one of the three components neads service during the warranty period?

Explanation / Answer

here please revert if P(A1) =0.96 ; P(A2) =0.97 and P(A3)=0.70 cause these values are not clear from picture

a)

P(3 functions properly)=0.96*0.97*0.7=0.6518

b)

P(at least one needs service) =1-0.6518 =0.3482

c)

P(all three need service) =(1-0.96)*(1-0.97)*(1-0.70)=0.0004

d)

P(only receiver needs servicee)=(1-0.96)*0.97*0.7=0.0272

e)

P(exactly one needs service)=P(receiver require service)+P(speaker needs service)+P(CD player needs service)=(1-0.96)*0.97*0.7+0.96*(1-0.97)*0.7+0.96*0.97*(1-0.7)=0.3267

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