SOLUTION: 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 ra

Question 1027105: 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 by mathmate(429) (Show Source): You can put this solution on YOUR website!

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?

Solution:
An efficient way to approach these problems is
1. define events
2. express all given information in terms of events
3. using known relationships, determine the unknown.

1. define events:
B=student has blue eyes
D=student has dark hair

2. express given information in terms of events
P(B)=0.70
P(D)=0.45
P(B∩D)=0.30

3. using known relationships (write down what you know), find unknown.
Assume random sampling.
P(D|B)=Probability of a randomly selected student has dark hair given she has blue eyes
=P(D∩B)/P(B) [ by definition of conditional probability ]
=0.30/0.70
= 3/7
= 42.8%
Answer: The required probability is 42.8%

I will leave it to you to round to the nearest whole percent, as specified in the question.
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