Statistics And Probability Question 487
Question: If X follows a binomial distribution with parameters $ n=6 $ and $ p $ and $ 4,(P(X=4))=P(X=2), $ then $ p= $
[EAMCET 1994]
Options:
A) $ \frac{1}{2} $
B) $ \frac{1}{4} $
C) $ \frac{1}{6} $
D) $ \frac{1}{3} $
Show Answer
Answer:
Correct Answer: D
Solution:
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$ 4P(X=4)=P(X=2)\Rightarrow 4.{}^{6}C_4p^{4}q^{2}={}^{6}C_2p^{2}q^{4} $
$ \Rightarrow 4p^{2}=q^{2}\Rightarrow 4p^{2}={{(1-p)}^{2}} $
$ \Rightarrow 3p^{2}+2p-1=0\Rightarrow p=\frac{1}{3} $ .
BETA
