Probability
Optimization of expression in P(A)
MMTS_Full_Test_09
Grade 12
Question:
If $A$ is any event in a sample space, the maximum value of $3\sqrt{P(A)}+4\sqrt{P(A')}$ is
(A) 4
(B) 2
(C) 5
(D) Cannot be determined
Step-by-Step Solution
Key Concept: Let $p=P(A)$. Maximize $f(p)=3\sqrt{p}+4\sqrt{1-p}$ on $[0,1]$. $f'(p)=0\Rightarrow p=9/25$. $f(9/25)=9/5+16/5=5$.
Max $=5$.
Correct Answer: (C) 5