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Question
A girl is preparing for National Level Entrance exam and State Level Entrance exam for professional courses. The chances of her cracking National Level exam is 0.42 and that of State Level exam is 0.54. The probability that she clears both the exams is 0.11. Find the probability that
- She cracks at least one of the two exams
- She cracks only one of the two
- She cracks none.
Solution
Let event A: The girl cracks the National Level exam.
∴ P(A) = 0.42
Let event B: The girl cracks the State Level exam.
∴ P(B) = 0.54
Also, P(A ∩ B) = 0.11
(i) P(the girl cracks at least one of the two exams)
= P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
= 0.42 + 0.54 – 0.11
= 0.85
(ii) P(the girl cracks only one of the two exams)
= P(A) + P(B) - 2P(A ∩ B)
= 0.42 + 0.54 - 2(0.11)
= 0.74
(iii) P(the girl cracks none of the exams)
= P(A' ∩ B')
= P(A ∪ B)'
= 1 - P(A ∪ B)
= 1 - 0.85
= 0.15
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