Let's denote the following probabilities:
P(boy) = 0.70 (since 70% of the class is boys)
P(girl) = 0.30 (since 30% of the class is girls)
P(blue eyes | boy) = 0.02 (2% of boys have blue eyes)
P(blue eyes | girl) = 0.03 (3% of girls have blue eyes)
We are looking to find the probability that the selected student is a girl given that they have blue eyes. This can be calculated using Bayes' Theorem:
P(girl | blue eyes) = P(girl) * P(blue eyes | girl) / P(blue eyes)
First, calculate the probability of having blue eyes in the class:
P(blue eyes) = P(boy) * P(blue eyes | boy) + P(girl) * P(blue eyes | girl)
P(blue eyes) = 0.70 * 0.02 + 0.30 * 0.03
P(blue eyes) = 0.014 + 0.009
P(blue eyes) = 0.023
Now, calculate the probability that the selected student is a girl given they have blue eyes:
P(girl | blue eyes) = P(girl) * P(blue eyes | girl) / P(blue eyes)
P(girl | blue eyes) = 0.30 * 0.03 / 0.023
P(girl | blue eyes) = 0.009 / 0.023
P(girl | blue eyes) = 0.3913
Therefore, the probability that the student is a girl given they have blue eyes is approximately 0.3913 or 39.13%.
In a class, 2% of the boys and 3% of girls are having blue eyes. There are 70% boys in the class. A student is selected and having blue eyes. What is the probability that
the student is girl
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