GATE 2023 ST – Question 60
On Ω={1,2,3,4},let 𝒢={∅,Ω,{1},{4},{2,3},{1,4},{1,2,3},{2,3,4}}. Suppose P({1})=1/4 and X(1)=1,X(2)=X(3)=2,X(4)=3. If P(X≤2)=3/4,find P({1,4}) to two decimals.
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Correct answer: 0.49 to 0.51
Explanation
The complement of {X≤2} is {4},so P({4})=1−3/4=1/4. The disjoint union {1,4} has probability 1/4+1/4=**0.50**.