Q. 135.0( 2 Votes )
The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75. What is the probability of passing the Hindi examination?
Answer :
Let E denotes the event that student passes in English examination.
And H be the event that student passes in Hindi exam.
Given,
P(E) = 0.75
P(passing both) = P(E ∩ H) = 0.5
P(passing neither) = P(E’ ∩ H’) = 0.1
P(H) = ?
As, we know that P(A’ ∩ B’) = P(A ∪ B)’ {using De Morgan’s law}
∴ P(E’ ∩ H’) = P(E ∪ H)’
⇒ 0.1 = 1 – P(E ∪ H)
⇒ P(E ∪ H) = 1 – 0.1 = 0.9
Note: By definition of P(A or B) under axiomatic approach(also called addition theorem) we know that:
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
∴ P(E ∪ H) = P(E) + P(H) – P(E ∩ H)
⇒ 0.9 = 0.75 + P(H) – 0.5
⇒ 1.4 – 0.75 = P(H)
∴ P(H) = 0.65
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