Answer:
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
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
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% [tex]=\frac{70}{100}[/tex] [tex]=\frac7{10}[/tex]
P(B)=45% [tex]=\frac{45}{100}[/tex] [tex]=\frac9{20}[/tex]
P(A∩B)=30%[tex]=\frac{30}{100}[/tex] [tex]=\frac3{10}[/tex]
∴P(B|A)
[tex]=\frac{P(A\cap B)}{P(A)}[/tex]
[tex]=\frac{0.3}{0.7}[/tex]
[tex]=\frac37[/tex]
=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%.
