KCET · Maths · Probability
If ' \( X \) ' has a binomial distribution with parameters \( n=6, p \) and \( P(X=2)=12, P(X=3)=5 \) then
\( P= \)
- A \( \frac{16}{21} \)
- B \( \frac{5}{16} \)
- C \( \frac{5}{12} \)
- D none
Answer & Solution
Correct Answer
(D) none
Step-by-step Solution
Detailed explanation
Given Options are not matching
\(\mathrm{n}=6\)
\(P(x=r)={ }^{n} C_{r} q^{n-r} p^{r}\)
\(P(x=2)=12\)
\({ }^{6} C_{2} q^{4} p^{2}=12\)
\(P(x=3)=5\)
\({ }^{6} C_{3} q^{3} p^{3}=5\)
\(\frac{(1)}{(2)} \Rightarrow \frac{{ }^{6} C_{2} q^{4} p^{2}}{{ }^{6} C_{3} q^{3} p^{3}}=\frac{12}{5}\)
\(\frac{15 q}{20 p}=\frac{12}{5}\)
\(75 q=240 p\)
\(75(1-p)=240 p\)
\(75-75 p=240 p\)
\(75=315 p\)
\(p=\frac{75}{315}=\frac{5}{21}\)
\(\mathrm{n}=6\)
\(P(x=r)={ }^{n} C_{r} q^{n-r} p^{r}\)
\(P(x=2)=12\)
\({ }^{6} C_{2} q^{4} p^{2}=12\)
\(P(x=3)=5\)
\({ }^{6} C_{3} q^{3} p^{3}=5\)
\(\frac{(1)}{(2)} \Rightarrow \frac{{ }^{6} C_{2} q^{4} p^{2}}{{ }^{6} C_{3} q^{3} p^{3}}=\frac{12}{5}\)
\(\frac{15 q}{20 p}=\frac{12}{5}\)
\(75 q=240 p\)
\(75(1-p)=240 p\)
\(75-75 p=240 p\)
\(75=315 p\)
\(p=\frac{75}{315}=\frac{5}{21}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The eccentricity of the ellipse \( \frac{x^{2}}{36}+\frac{y^{2}}{16}=1 \) isKCET 2017 Easy
- The area of the region bounded by \( y \)-axis. \( y=\cos x \) and \( y=\sin x ; 0 \leq x \leq \frac{\pi}{2} \) isKCET 2019 Easy
- The area of the region bounded by \(y=2 x-x^{2}\) and the \(x\)-axis isKCET 2008 Easy
- \(\int \frac{1}{1+3 \sin ^2 x+8 \cos ^2 x} d x\) is equals toKCET 2023 Hard
- The value of \(\int \frac{1+x^{4}}{1+x^{6}} d x\) isKCET 2020 Medium
- A die has two face each with number ' 1 ', three faces each with number ' 2 ' and one face with number ' 3 '. If the die is rolled once, then \(\mathrm{P}(1\) or 3\()\) isKCET 2025 Easy
More PYQs from KCET
- The domain of the function defined by \(f(x)=\cos ^{-1} \sqrt{x-1}\) isKCET 2020 Easy
- For what distance is ray optics is good approximation when the aperture is \( 4 \mathrm{~mm} \) and the
wavelength of light is \( 400 \mathrm{~nm} \) ?KCET 2016 Medium - If \(|\mathbf{a}|=2\) and \(|\mathbf{b}|=3\) and the angle between \(\mathbf{a}\) and \(\mathbf{b}\) is \(120^{\circ}\), then the length of the vector \(\left|\frac{\mathbf{a}}{2}-\frac{\mathbf{b}}{3}\right|\) isKCET 2022 Medium
- Given below and the atomic masses of the elements:
\begin{array}{|l|l|l|l|l|l|l|l|l|l|}
\hline \text { Element: } & \mathrm{Li} & \mathrm{Na} & \mathrm{Cl} & \mathrm{~K} & \mathrm{Ca} & \mathrm{Br} & \mathrm{Sr} & \mathrm{I} & \mathrm{Ba} \\
\hline \text { Atomic Mas }\left(\mathrm{g} \mathrm{~mol}^{-1}\right): & 7 & 23 & 35.5 & 39 & 40 & 80 & 88 & 127 & 137 \\
\hline
\end{array}
Which of the following doesn't form triad?KCET 2025 Easy - Which of the following is correct with respect to melting point of a transition element?KCET 2023 Medium
- The correct equation depicting species-area relationship isKCET 2021 Medium