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Question 19
Over the past 200 working days, the number of defective parts produced by a machine is given in the following table.

Number of012345678910111213defective partsDays503222181212101010108662

Determine the probability that tomorrow’s output will have:
(i)
No defective part.
(ii) Atleast one defective part.
(iii) Not more than 5 defective parts.
(iv) More than 13 defective parts.

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Solution

Total number of working days, n(S) = 200

(i) Number of days in which no part is defective, n(E1)=50
Probability of no defective part is, 50200=0.25

(ii) Number of days in which atleast one part is defective,
n(E2)=32+22+18+12+12+10+10+10+8+6+6+2+2=150
Probability that atleast one defective part =n(E2)n(S)=150200=34=0.75
Hence, the probability of least one defective part is 0.75.

(iii) Number of days in which not more than 5 parts aredefective,
n(E3)=50+32+22+18+12+12=146
Probability of not more than 5defective parts =n(E3)n(S)=146200=0.73

(iv) Number of days in which not more than 13defective parts,
n(E4)=0
Probability for more than 13 defective parts =n(E4)n(S)=0200=0
Hence, the probability of more than 13 defective parts is 0.

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