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प्रश्न
In a college, 70% of students pass in Physics, 75% pass in Mathematics and 10% of students fail in both. One student is chosen at random. What is the probability that:
(i) He passes in Physics and Mathematics?
(ii) He passes in Mathematics given that he passes in Physics.
(iii) He passes in Physics given that he passes in Mathematics.
उत्तर
Let x% of students pass in both Physics and Mathematics
Students pass in Physics = 70% ⇒ P (P) = `(70)/(100)`
Students pass in Mathematics = 75% ⇒ P (M) = `(75)/(100)`
Students fail in both = 10%
Now students pass in physics only + students pass in mathematics only + students pass in both physics and mathematics = 90%
⇒ 70% - x + x + 75% - x = 90%
x = 55% ⇒ P (M ∩ P) = `(55)/(100)`
(i)
P ( Passes in Physics and Mathematics) = `(55)/(100) = (11)/(20)`
(ii)
P (M/P) = `(P (M ∩ P))/(P(P)`
= `((55)/(100))/(70/(100))`
= `(55)/(70) = (11)/(14)`
(iii)
`P(P/M) = (P(M ∩ P))/(P(M))`
`(55/100)/(75/100)`
= `55/75 = 11/15`
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