star electronics,inc. received two supplies of the same type components for thei

Question

star electronics,inc. received two supplies of the same type components for their production, 150,000 components from supplier #1 and 50,000 components from supplier #2. both supplies were randomly mixed up in one big storage. later, star elecronics,inc. has figured out that the components from supplier #2 cannot be used for production due to their design incompatibility. star electronics plans to make four devices, each uses one of the supplied components. all four components for four devices were randomly picked from the supply storage.

what is the probability that at least 3 of 4 produced devices would properly function?(in others words,what is the probablity that at least 3 of 4 randomly picked components are from supplier #1?).

Explanation / Answer

P(S1) =P(component choosen is from supplier 1) = no of components supplied by 1/ total no of component supplied

= 150,000/150,000+50,000 =150,000/200,000 = 0.75

P(S2) =P(component choosen is from supplier 2) =no of components supplied by 1/ total no of component supplied

= 50,000/200000 = 0.25

P(at least 3 of 4 produced devices would properly function) =P(3 of 4 produced devices would properly function) + P( 4 of 4 produced devices would properly function )

= S1*S1*S1*S2 + S1*S1*S1*S1

= 0.75*0.75*0.75*0.25 + 0.75*0.75*0.75*0.75

= 0.105 + 0.316

= 0.421

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