Question

3% of bolts produced by a company are defective . Find probability that in a pack of 100 bolts ,2 are defective a)0.322 b) 0.434 c)0.224 d) 0.352​

Answer 1

Step-by-step explanation:

In a bolt factory, three machines A, B and C manufacture 25, 35 and 40 percent of the total bolts respectively. Out of the total bolts manufactured by the machines 5, 4 and 2 percent are defective from machine A, B and C respectively. A bolt drawn at random is found to be defective. Find the probability that it was manufactured by (i) Machine A or C (ii) Machine B.

Answer 2

Answer:-

Bolts manufactured from machine A = 25%

Bolts manufactured from machine B = 35%

Bolts manufactured from machine C = 40%

So, probability of bolt manufactured by machine A=P(A)=25100=0.25

Probability of bolt manufactured by machine B=P(B)=35100=0.35

Probability of bolt manufactured by machine C=P(C)=40100=0.40

Now, probability of a defective bolt manufactured by machine A=P(D|A)=5100=0.05

Probability of a defective bolt manufactured by machine B=P(D|B)=4100=0.04

Probability of a defective bolt manufactured by machine C=P(D|C)=2100=0.02

Now, we know that according to Bayes theorem;

P(A|B)=P(B|A).P(A)P(B)

Where;

A,B= events

P(A|B)= probability of B given A is true

P(A),P(B)= The independent probability of A and B

So,

P(B|D)=P(B).P(D|B)P(A).P(D|A)+P(B).P(D|B)+P(C).P(D|C)

Where D means bolt is defective

P(B|D)=0.35×0.040.25×0.05+0.35×0.04+0.4×0.02=0.0140.0125+0.014+0.008=0.0140.0345=140345=2869

Therefore, probability that it was manufactured by machine B is 2869

Now, for is part we have to find the probability that it was manufactured by machine A or C. It is same as the probability that is not manufactured by B. Therefore, probability it was manufactured by machine A or C;

=1−P(B|D)

=1−2869=69−2869=4169

Note: These types of questions are formula based so remembering the formula of Baye’s theorem will be helpful, also it becomes easier to solve (i) part by solving (ii) first.

Hope it's helpful..!!

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