Question

In a city school, 70% of students have blue eyes, 45% have dark hair, and 30% have blue eyes and dark hair. What is the probability (rounded to the nearest whole percent) that a randomly selected student has dark hair, given that the student has blue eyes

Answer 1

The probability that a randomly selected student has dark hair, given that the student has blue eyes is 43%.

Explanation:

Conditional probability:

Let A and B any two events connected to a given random experiment E. The conditional probability of the event A on the hypothesis that the event B has occurred, denoted by P(A|B), is defined as

`P(A|B)=(P(A\cap B))/(P(B))`

Given that,

In a city school, 70% of students have blue eyes, 45% have dark eyes and 30% have blue eyes and dark hair.

A= students have blue eyes

B= Students have dark hair.

P(A)= 70%
`=(70)/(100)`
`=\frac7{10}`

P(B)=45%
`=(45)/(100)`
`=\frac9{20}`

P(A∩B)=30%
`=(30)/(100)`
`=\frac3{10}`

∴P(B|A)

`=(P(A\cap B))/(P(A))`

`=(0.3)/(0.7)`

`=\frac37`

=0.429

=0.429×100 %

≈43%

The probability that a randomly selected student has dark hair, given that the student has blue eyes is 43%.