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प्रश्न
Two-third of the students in a class are boys and rest are girls. It is known that the probability of girl getting first class is 0.25 and that of boy getting is 0.28. Find the probability that a student chosen at random will get first class.
उत्तर
Let A be the event that student chosen is a boy
B be the event that student chosen is a girl
C be the event that student gets first class
∴ P(A) = `2/3`, P(B) = `1/3`
Probability of student getting first class, given that student is boy
Probability of student getting first class given that student is a girl, is
`"P"("C"/"A") = 0.28 = 28/100 and "P"("C"/"B") = 0.25 = 25/100`
∴ Required probability = P((A ∩ C) ∪ (B ∩ C))
Since A ∩ C and B ∩ C are mutually exclusive events
∴ Required probability = P(A ∩ C) + P(B ∩ C)
= `"P"("A")*"P"("C"/"A") + "P"("B")*"P"("C"/"B")`
= `(2/3 xx 28/100) + (1/3 xx 25/100)`
= `(56 + 25)/300`
= `81/300`
= `27/100`
= 0.27
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