GATE ME 2025 Set 1 — Question 10
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Engineering Mathematics → Probability → Axioms of Probability
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Question
A final year student appears for placement interview in two companies, S and T. Based on her interview performance, she estimates the probability of receiving job offers from companies S and T to be 0.8 and 0.6, respectively. Let be the probability that she receives job offers from both the companies. Select the most appropriate option.
Correct answer
(B) 0.4 ≤ p ≤ 0.6
Solution
Let and be the probabilities of receiving job offers from companies S and T respectively. Let be the probability of receiving offers from both.
According to the principle of inclusion-exclusion:
Since probability cannot exceed 1, :
Also, the probability of the intersection of two events cannot exceed the probability of either event:
Combining these, we get .
According to the principle of inclusion-exclusion:
Since probability cannot exceed 1, :
Also, the probability of the intersection of two events cannot exceed the probability of either event:
Combining these, we get .
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