MHT CET · Maths · Probability
It is known that a box of 8 batteries contains 3 defective pieces and a person randomly selects two batteries from the box. If \(X\) is the number of defective batteries selected,
then \(P(X \leq 1)=\)
- A \(\frac{25}{28}\)
- B \(\frac{14}{28}\)
- C \(\frac{10}{28}\)
- D \(\frac{13}{28}\)
Answer & Solution
Correct Answer
(A) \(\frac{25}{28}\)
Step-by-step Solution
Detailed explanation
We have probability of selecting defective batteries \(=\frac{3}{8}\)
\(\therefore p=\frac{3}{8} \text { and } q=\frac{5}{8} \)
\( \therefore P(X=0)+P(X=1) \)
\( =\left[{ }^{2} C_{0}\left(\frac{3}{8}\right)^{0} \times\left(\frac{5}{8}\right)^{2}\right]+\left[{ }^{2} C_{1}\left(\frac{3}{8}\right)^{1} \times\left(\frac{5}{8}\right)^{1}\right] \)
\( =\frac{25}{64}+\frac{2 \times 3 \times 5}{64}=\frac{55}{64} \)
\(\therefore p=\frac{3}{8} \text { and } q=\frac{5}{8} \)
\( \therefore P(X=0)+P(X=1) \)
\( =\left[{ }^{2} C_{0}\left(\frac{3}{8}\right)^{0} \times\left(\frac{5}{8}\right)^{2}\right]+\left[{ }^{2} C_{1}\left(\frac{3}{8}\right)^{1} \times\left(\frac{5}{8}\right)^{1}\right] \)
\( =\frac{25}{64}+\frac{2 \times 3 \times 5}{64}=\frac{55}{64} \)
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
- If \(\mathrm{A}=\left[\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}\right]\) and \(\mathrm{A}^{-1}=\mathrm{KA}\), then \(\mathrm{K}\) isMHT CET 2021 Easy
- The number of distinct real values of \(\lambda\), for which the vectors \(-\lambda^2 \hat{i}+\hat{j}+\hat{k}, \hat{i}-\lambda^2 \hat{j}+\hat{k}\) and \(\hat{i}+\hat{j}-\lambda^2 \hat{k}\) are coplanar, isMHT CET 2024 Easy
- If \(\mathrm{f}(x)=\log _{x^2}\left(\log _{\mathrm{e}} x\right)\), then \(\mathrm{f}^{\prime}(x)\) at \(x=\mathrm{e}\) isMHT CET 2024 Easy
- Let \(Z\) be a complex number such that \(|Z|+Z=2+i(\) where \(i=\sqrt{-1})\), then \(|Z|\) is equal toMHT CET 2024 Medium
- The area bounded by the parabola \(y^{2}=x\), straight line \(y=4\) and \(y\) -axis is square units isMHT CET 2011 Easy
- If cartesian equation of the line is \(x-1=2 y+3=3-z\), then its vector equation
isMHT CET 2020 Easy
More PYQs from MHT CET
- If \(m_{1}\) and \(m_{2}\) are the slopes of tangents to the circle \(x^{2}+y^{2}=4\) from the point \((3,2)\), then \(m_{1}-m_{2}\) is equal toMHT CET 2009 Hard
- The general solution of differential equation \(\frac{d y}{d x}=e^{x+y}+x^2 e^{x^3+y}\) is (where \(\mathrm{C}\) is a constant of integration.)MHT CET 2022 Hard
- A particle starts from mean position and performs S.H.M. with period 6 second. At what time its kinetic energy is \(50 \%\) of total energy? \(\left(\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right)\)MHT CET 2020 Easy
- Which of the following forces is involved in dinitrogen?MHT CET 2025 Easy
- In \(\triangle \mathrm{ABC}\), with usual notations, if \(\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}\), then the value of \(\cos \mathrm{A}+\cos \mathrm{B}+\cos \mathrm{C}\) isMHT CET 2023 Medium
- The pH of a sample of vinegar is 3.76. Calculate the concentration of hydrogen ion in it in \(\mathrm{mol~} \mathrm{dm}^{-3}\) ?MHT CET 2025 Easy