Probability Question 228

Question: A sample space consists of 3 sample points with associated probabilities given as $ 2p,p^{2},4p-1 $ . Then the value of p is

Options:

A) $ p=\sqrt{11}-3 $

B) $ \sqrt{10}-3 $

C) $ \frac{1}{4}<p<\frac{1}{2} $

D) none

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Answer:

Correct Answer: A

Solution:

$ p^{2}+2p+4p-1=1 $ (Exhaustive) $ p^{2}+6p-2=0 $ Or $ p=-3\pm \sqrt{11}=\sqrt{11}-3 $