Question

A recent survey found that the ages of workers in a factory is distributed as follows:

Age (in years)	20 – 29	30 – 39	40 – 49	50 – 59	60 and above
Number of workers	38	27	86	46	3

If a person is selected at random, find the probability that the person is:

1. 40 years or more
2. under 40 years
3. having age from 30 to 39 years
4. under 60 but over 39 years

Answer 1

Total number of workers in a 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(E_1) = (n(E_1))/(n(S))` 

= `135/200`

= 0.675

Hence, the probability that the person selected at the age of 40 years or more is 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(E_2) = (n(E_2))/(n(S))` 

= `65/200`

= 0.325

Hence, the probability that the persons selected under the age of 40 years is 0.325.

iii. Number of persons selected having age from 30 to 39 years,

n(E₃) = 27

∴ Probability that the person selected having age from 30 to 39 years,

`P(E_3) = (n(E_3))/(n(S))` 

= `27/200`

= 0.135

Hence, the probability that the person selected having age from 30 to 39 years is 0.135.

iv. Number of persons selected having age under 60 but over 39 years,

n(E₄) = 86 + 46 = 132

∴ Probability that the person selected having age under 60 but over 39 years,

`P(E_4) = (n(E_4))/(n(S))` 

= `132/200`

= 0.66

Hence, the probability that the person selected having age under 60 but over 39 years is 0.66.