Question

it is known that 20% of the males and 5% of the females are unemployed in a certain town consisting of equal number of males and females a person is selected at random and found to be unemployed what is the probability that the selected on a person is male and female​

Answer 1

Answer:

35 pecent it is female because women's are least unemployment

Answer 2

Correct -Question

it is known that 20% of the males and 5% of the females are unemployed in a certain town consisting of an equal number of males and females a person is selected at random and found to be unemployed what is the probability that the selected a person is an option(1) male and option(2) female.

Answer:

Option(1). An unemployed person is selected at random, the probability that the selected person is male is $\frac{4}{5}$.

Option(2) An  unemployed person is selected at random, the probability that the selected person is female is $\frac{1}{5}$.

Step-by-step explanation:

Given:

20% of the males and 5% of the females are unemployed in a certain town.

The number of males and females are equal.

At random a person is selected and found to be unemployed.

To Find:

An unemployed person is selected at random, the probability that the selected person is male.

An unemployed person is selected at random, the probability that the selected person is female.

Solution:

Considering - Option(1). An unemployed person is selected at random, the probability that the selected person is male.

Let the events M, F, and U be defined as per the following:

M: A male is selected

F: A female is selected

U: A person is unemployed.

As given - the number of males and the number of females are equal.

P(M)=P(F)=1/2

Now, P(U/M)= Probability of selecting an unemployed person given that they are male  $=20\%=\frac{20}{100} =\frac{1}{5}$

P(U/F)= Probability of selecting an unemployed person given that they are female  $=5\%=\frac{5}{100} =\frac{1}{20}$

An unemployed person is selected at random, the probability that the selected  a person is  male =P(M∣U)

$=\frac{P(M)\times P(U|M)}{(P(F)\times P(U|F)+P(M)\times P(U|M) }$    using Baye's theorem.

$=\frac{\frac{1}{2}\times \frac{1}{5} }{({\frac{1}{2}\times \frac{1}{5} } +{\frac{1}{2}\times \frac{1}{20} } )}$

$=\frac{\frac{1}{10}}{({\frac{1}{10} } +{\frac{1}{40} } )}$

$=\frac{\frac{1}{10}}{{\frac{(4+1)}{40} } }=\frac{\frac{1}{10}}{{\frac{5}{40} } }$

$=\frac{4}{5}$

Thus, an  unemployed person is selected at random, the probability that the selected person is  male is 4/5.

Considering - Option(2). An unemployed person is selected at random, the probability that the selected person is female.

An unemployed person is selected at random, the probability that the selected  a person is female =P(F∣U)

$=\frac{P(F)\times P(U|F)}{(P(F)\times P(U|F)+P(M)\times P(U|M) }$   using Baye's theorem.

$=\frac{\frac{1}{2}\times \frac{1}{20} }{({\frac{1}{2}\times \frac{1}{5} } +{\frac{1}{2}\times \frac{1}{20} } )}$

$=\frac{\frac{1}{40}}{({\frac{1}{10} } +{\frac{1}{40} } )}$

$=\frac{\frac{1}{40}}{{\frac{(4+1)}{40} } }=\frac{\frac{1}{40}}{{\frac{5}{40} } }$

$=\frac{1}{5}$

Thus, an  unemployed person is selected at random, the probability that the selected person is female is 1/5.