SOLUTION: 66% of students In a class are boys and rest are girls it is known that the probability of a girl getting a first class is 0.25 and that a boy getting first class in 0.28 find the

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Question 1019578: 66% of students In a class are boys and rest are girls it is known that the probability of a girl getting a first class is 0.25 and that a boy getting first class in 0.28 find the probability that a student selected at random will get first class marks in the subject
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Question:
66% of students In a class are boys and rest are girls it is known that the probability of a girl getting a first class is 0.25 and that a boy getting first class in 0.28 find the probability that a student selected at random will get first class marks in the subject

Solution:
Hint: use law of total probability.
Proportion of boys (B): 66%
proportion of girls (G): 100-66=34%
Let
F=event of getting first class, then

P(F|B)=0.28 (probability of getting first class given that it's a boy)
P(F|B)=P(F∩B)/P(B), therefore P(F∩B)=0.28*0.66=0.1848

P(F|G)=0.25 (probability of getting first class given that it's a girl)
P(F|G)=P(F∩G)/P(G), therefore P(F∩G)=0.25*0.34=0.085

Therefore probability of getting first class out of the whole class
P(F)
=P(F∩(B∪G))
=P(F∩B)+P(F∩G) [since boys and girls are mutually exclusive]
=0.1848+0.085
=0.2698