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Question

# Question 20 A recent survey found that ages of workers in a factory as follows: Age(in years)20−2930−3940−4950−5960 and aboveNumber of382786463workers If a person is selected at random, find the probability that the person is: (i) 40 years or more. (ii) Under 40 years. (iii) Having age from 30 - 39 years. (iv) Under 60 but over 39 years.

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Solution

## Total number of workers in the factory, n(S)=38+27+86+46+3=200 (i) Number of persons selected at the age of 40 years or more, n(E1)=86+46+3=135 ∴ Probability that the persons selected at the age of 40 years or more, P(E1)=n(E1)n(S)=135200=0.675 (ii) Number of persons selected under the age of 40 years, n(E2)=38+27=65 ∴ Probability that the persons selected under the age of 40 years, P(E1)=n(E2)n(S)=65200=0.325 (iii) Number of persons selected having age from 30 to 39 years, n(E3)=27 ∴ Probability that the persons selected having age from 30 to 39 years, P(E3)=n(E3)n(S)=27200=0.135 (iv) Number of persons selected having age under 60 nut over 39 years, n(E4)=86+46=132 ∴ Probability that the persons selected having age under 60 but over 39 years, P(E4)=n(E4)n(S)=132200=0.66

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