MHT CET · Maths · Probability
If the sum of the mean and the variance of a Binomial distribution for 5 trials is 1.8 , then the value of \(\mathrm{p}\) is
- A 0.4
- B 0.8
- C 0.18
- D 0.2
Answer & Solution
Correct Answer
(D) 0.2
Step-by-step Solution
Detailed explanation
According to the given condition,
mean + variance \(=1.8\)
\(\begin{aligned} & \Rightarrow n p+n p q=1.8 \\ & \Rightarrow 5 p+5 p q=1.8 \\ & \Rightarrow 5 p+5 p(1-p)=1.8 \\ & \Rightarrow 5 p+5 p-5 p^2=1.8 \\ & \Rightarrow 5 p^2-10 p+1.8=0 \\ & \Rightarrow 50 p^2-100 p+18=0 \\ & \Rightarrow(10 p-2)(5 p-9)=0 \\ & \Rightarrow p=\frac{2}{10}=0.2 \text { or } p=\frac{9}{5}=1.8\end{aligned}\)
Since \(0 < \mathrm{p} < 1\),
\(\mathrm{p}=0.2\)
mean + variance \(=1.8\)
\(\begin{aligned} & \Rightarrow n p+n p q=1.8 \\ & \Rightarrow 5 p+5 p q=1.8 \\ & \Rightarrow 5 p+5 p(1-p)=1.8 \\ & \Rightarrow 5 p+5 p-5 p^2=1.8 \\ & \Rightarrow 5 p^2-10 p+1.8=0 \\ & \Rightarrow 50 p^2-100 p+18=0 \\ & \Rightarrow(10 p-2)(5 p-9)=0 \\ & \Rightarrow p=\frac{2}{10}=0.2 \text { or } p=\frac{9}{5}=1.8\end{aligned}\)
Since \(0 < \mathrm{p} < 1\),
\(\mathrm{p}=0.2\)
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