MHT CET · Maths · Probability
A random variable has the following probability distribution
The then value of \(p\) is
- A \(\frac{1}{10}\)
- B \(\frac{1}{30}\)
- C \(\frac{1}{100}\)
- D \(\frac{3}{20}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{10}\)
Step-by-step Solution
Detailed explanation
\(\text { Here, } \)
\( 0+2 p+2 p+3 p+p^2+2 p^2+7 p^2+2 p=1 \)
\( \therefore 9 p+10 p^2=1 \)
\( \therefore 10 p^2+9 p-1=0 \)
\( \therefore 10 p^2+10 p-p-1=0 \)
\( \therefore 10 p(p+1)-1(p+1)=0 \)
\( \therefore p=\frac{1}{10} \text { or } p=-1 \)
\( \text { But } 0 \leq p \leq 1 \)
\( \therefore p=\frac{1}{10}\)
\( 0+2 p+2 p+3 p+p^2+2 p^2+7 p^2+2 p=1 \)
\( \therefore 9 p+10 p^2=1 \)
\( \therefore 10 p^2+9 p-1=0 \)
\( \therefore 10 p^2+10 p-p-1=0 \)
\( \therefore 10 p(p+1)-1(p+1)=0 \)
\( \therefore p=\frac{1}{10} \text { or } p=-1 \)
\( \text { But } 0 \leq p \leq 1 \)
\( \therefore p=\frac{1}{10}\)
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