Question

suppose 5% of men and 0.25% of women have grey hair A grey haired person is selected at random What is the probability of this person being male ? assume that there are equal number of males and females

Answer 1

Let E1E1 be the event that the selected person is male and E2E2 be the event that its a female.

P(E1)=12=P(E1)=12=P(E2)P(E2)

E1E1 and E2E2 are mutually exclusive and exhaustive, so we can apply Bayes theorem.

Let E: be the event that the person has grey hair. 5% of men picked at random have grey hair →P(EE1)=5100=120→P(EE1)=5100=120

We can calcuate the probability: P(E1E)=P(EE1).P(E1)(P(EE1).P(E1))+(P(EE2).P(E2))P(E1E)=P(EE1).P(E1)(P(EE1).P(E1))+(P(EE2).P(E2))

P(E1E)=1201212012+140012=2021P(E1E)=1201212012+140012=2021

 hope hpfl...

  

Answer 2

Answer:

= $\frac{20}{21}$

Step-by-step explanation:

Let E₁ , E₂ and A be events such that

E₁ = Selecting male person

E₂ = Selecting women (female person)

A = Selecting grey haired person

Then, P(E₁) = 1/2 ,                          P(E₂) = 1/2

      P(A/E₁) = 5/100                        P(A/E₂) = 0.25 / 100

Here, Required probability is P(E₁/A)

               P(E₁/A) = P(E₁) . P(A/E₁) / P(E₁) . P(A/E₁) + P(E₂) . P(A/E₂)

         => P(E₁/A) = 1/2 × 5/100 / 1/2 × 5/100 + 1/2 × 0.25/100

         => 5 / 5 + 0.25

         => 500 / 525

         => $\frac{20}{21}$

GOOD LUCK !!