GATE 2014 CS (CS3) – Question 58
A and B are mutually exclusive events in sample space S with $A\cup B=S$. Find the maximum of P(A)P(B).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0.25 to 0.25
Explanation
Disjoint exhaustive events have probabilities p and1−p. Their product p(1−p)=1/4−(p−1/2)²is at most1/4, attained when both equal1/2. Thus maximum **0.25**. Mutual exclusivity alone would not give their sum1without exhaustiveness.