COMEDK · Maths · 36. Probability
A and B are two independent events. The probability of their simultaneous occurrence is \(\dfrac{1}{8}\) and the probability that neither of them occurs is \(\dfrac{3}{8}\). Then their individual probabilities are
- A \(\dfrac{3}{8} \text { and } \dfrac{1}{8}\)
- B \(\dfrac{5}{8} \text { and } \dfrac{1}{4}\)
- C \(\dfrac{3}{4} \text { and } \dfrac{1}{2}\)
- D \(\dfrac{1}{2} \text { and } \dfrac{1}{4}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{1}{2} \text { and } \dfrac{1}{4}\)
Step-by-step Solution
Detailed explanation
Let \(P(A) = x\) and \(P(B) = y\). Since \(A\) and \(B\) are independent events, \(P(A \cap B) = P(A)P(B) = xy = \dfrac{1}{8}\). The probability that neither occurs is \(P(A^{c} \cap B^{c}) = P(A^{c})P(B^{c}) = (1-x)(1-y) = \dfrac{3}{8}\). Expanding the second equation:…
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 feasible region represented by the constraints:
\(x + 2y \leq 120\);
\(x + y \geq 60\);
\(x - 2y \geq 0\);
\(x \geq 0\) and \(y \geq 0\)COMEDK 2026 Easy - \(\int \dfrac{1}{x \sqrt{a x-x^2}} d x\) isCOMEDK 2022 Hard
- Let \((3,4,-1)\) and \((-1,2,3)\) be the end points of a diameter of a sphere. Then, the radius of the sphere is equal toCOMEDK 2017 Easy
- The number of real roots of the equation
\(x^{4}+\sqrt{x^{4}+20}=22\) isCOMEDK 2014 Easy - \(\text { The point on the curve } x^2=x y \text { which is closest to }(0,5) \text { is }\)COMEDK 2024 Medium
- The shortest distance between the lines \(\frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1}\) and \(\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{4}\) is
\(\begin{array}{ll}\text { a. } \sqrt{30} \quad \text { b. } 2 \sqrt{30} & \text { c. } 5 \\ \lim _{x \rightarrow \infty}\left(\sqrt{a^{2} x^{2}+b x+x}-a x\right) & =\end{array}\)COMEDK 2015 Medium
More PYQs from COMEDK
- The solution of the differential equation \(\dfrac{d y}{d x}-y=1\) given \(y(0)=1\), isCOMEDK 2025 Medium
- If \(\lim _{x \rightarrow \infty}\left(1+\dfrac{a}{x}+\dfrac{b}{x^2}\right)^{2 x}=e^2\), thenCOMEDK 2022 Hard
- Mean life of a radioactive sample is \(100 \mathrm{~s}\). Then, its half-life (in min) isCOMEDK 2017 Easy
- A silicon sample is doped simultaneously with donor impurity phosphorus at a concentration of \(N_D = 3 \times 10^{22}\ m^{-3}\) and acceptor impurity boron at a concentration of \(N_D = 2.8 \times 10^{22}\ m^{-3}\). The intrinsic carrier concentration of silicon at room temperature is \(n_i = 1.5 \times 10^{16}\ m^{-3}\). Assuming complete ionization, the hole concentration is:
A. \(1.125 \times 10^{10}\ m^{-3}\)
B. \(1.125 \times 10^{11}\ m^{-3}\)
C. \(2.125 \times 10^{10}\ m^{-3}\)
D. \(2.125 \times 10^{11}\ m^{-3}\)COMEDK 2026 Medium - Alkyl halides undergoing \(\mathrm{S}_{\mathrm{N}} 2\) reaction do inverseCOMEDK 2022 Easy
- The ten's digit in
\(1 !+4 !+7 !+10 !+12 !+13 !+15 !+16 !+17 !\) is divisible byCOMEDK 2019 Hard