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

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

Step-by-step 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

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%

P(B)=45%

P(A∩B)=30%

∴P(B|A)

=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%.