In a certain town, male and female each form 50% of the population

Math Aug 04, 2020

In a certain town, male and female each form 50% of the population. It is known that 20% of the males and 5% of the females are unemployed. A research student studying the employment situation selects an unemployed person at random. What is the probability that the person so selected is: (a) male (b) Female

Expert Solution

This is a question of conditional probability

here, male and females population is 50% each.

and unemployed males and females are 20% and 5%.

Let males , females , unemployed denoted by M, F ,U respectively.

we can calculate,

the unemployed percentage of male = (50/100) * (20 / 100) = 0.10 = P(M)

the unemployed percentage of female = (50/100) * (5 / 100) = 0.025 = P(F)

Total unemployed population will be = 0.125

a.) P(M/U) = P( M ∩ U ) / P(U)

= 0.10/0.125

=0.8

b.) P(F/U) = P( F ∩ U ) / P(U)

= 0.025/0.125

=0.2

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