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  • A company has two machines, A and B, producing parts. Machine A produces 60% of the parts while Machine B produces the remaining 40%. The probability that a part produced by machine A is defective

A company has two machines, A and B, producing parts. Machine A produces 60% of the parts while Machine B produces the remaining 40%. The probability that a part produced by machine A is defective is 5%, while for machine B it is 3%. If a part is chosen at random, what is the probability that it is not defective?

Option: 1

0.0958


Option: 2

0.978


Option: 3

0.878


Option: 4

0.858


Answers (1)

best_answer

Let event A be the event that a part is produced by machine A, and event B be the event that a part is produced by machine B. Let event D be the event that a part is defective. 

We know that:

\\{P(A)=\frac{60}{100}}\\ \\\Rightarrow P(A)=\ 0.6

\\{P(B)=\frac{40}{100}}\\ \\\Rightarrow P(B)=\ 0.4

Since 5% parts of machine A is defective,

\\{P(D/A)=\frac{5}{100}}\\ \\\Rightarrow P(D/A)=\ 0.0.5

Now, 3% parts of machine B is defective,

\\{P(D/B)=\frac{3}{100}}\\ \\\Rightarrow P(D/B)=\ 0.0.3

We use the law of total probability to find the overall probability of a part being defective.

{P(D)=P(D/A)\times P(A)+\ P(D/B)\times P(B)}

Substituting the values, we get,

\\\Rightarrow {P(D)=0.05\times 0.6+\ 0.03\times 0.4}\\ \\\Rightarrow {P(D)=\ 0.042}

To find the probability that a part is not defective, we can use the complement rule:

\\{P\text{(not D)}=1-\ P(D)}\\ \\\Rightarrow {P\text{(not D)}=1-\ 0.042}\\ \\\Rightarrow { P\text{(not D)}=\ 0.958}\\

So, the probability of the part that is not defective, is 0.958.

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Rishabh

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