COMEDK · Maths · 36. Probability
If \(A, B\) and \(C\) are mutually exclusive and exhaustive events of a random experiment such that \(P(B)=\dfrac{3}{2} P(A)\) and \(P(C)=\dfrac{1}{2} P(B)\), then \(P(A \cup C)\) equals
- A \(\dfrac{10}{13}\)
- B \(\dfrac{3}{13}\)
- C \(\dfrac{6}{13}\)
- D \(\dfrac{7}{13}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{7}{13}\)
Step-by-step Solution
Detailed explanation
Since \(A, B,\) and \(C\) are mutually exclusive and exhaustive events, the sum of their probabilities is \(P(A) + P(B) + P(C) = 1\). Given \(P(B) = \dfrac{3}{2} P(A)\) and \(P(C) = \dfrac{1}{2} P(B)\), we can express \(P(C)\) in terms of \(P(A)\) as…
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
- \(\int \frac{x d x}{2(1+x)^{3 / 2}}\) is equal toCOMEDK 2023 Easy
- The angle between the lines \(\frac{x-2}{3}=\frac{y-1}{1}=\frac{z+3}{-1}\) and \(\frac{x+1}{2}=\frac{y-1}{-1}=\frac{z}{2}\) isCOMEDK 2024 Easy
- If \(X = \tan^{-1}\left[2\cos\left(2\sin^{-1}\dfrac{1}{2}\right)\right] + \cos^{-1}\left[\cos\left(\dfrac{7\pi}{6}\right)\right]\) and \(Y = \sin^{-1}\left[\sin\left(\dfrac{11\pi}{6}\right)\right] + \tan^{-1}\left[\tan\left(\dfrac{4\pi}{3}\right)\right]\) then the value of \(2X - Y\) is:COMEDK 2026 Medium
- The unit vector in the direction of the vector \(\mathbf{a}+2 \mathbf{b}-\mathbf{c}\) is equal toCOMEDK 2012 Easy
- Using mathematical induction, the numbers \(a_n s\) are defined by \(a_0=1, a_{n+1}=3 n^2+n+a_n\), \((n \geq 0)\). Then, \(a_n\) is equal toCOMEDK 2023 Medium
- Set \(A=\{x: x\) is a prime number less than 4\(\}\)
\(B=\left\{x: x^2-7 x-18=0, x \in R\right\}\)
Then set \(A\) and \(B\) areCOMEDK 2025 Medium
More PYQs from COMEDK
- The correct condition for physical adsorption isCOMEDK 2022 Easy
- \(\text { If } P=\left[\begin{array}{lll}
1 & \alpha & 3 \\
1 & 3 & 3 \\
2 & 4 & 4
\end{array}\right] \text { is the adjoint of a } 3 \times 3 \text { matrix } A \text { and }|A|=4 \text { then } \alpha \text { is equal to }\)COMEDK 2024 Medium - If the radius of earth were to shrink by two percent, its mass remaining the same, the acceleration due to gravity on the earth's surface wouldCOMEDK 2025 Easy
- If \(\tan \theta+\tan 4 \theta+\tan 7 \theta=\tan \theta \tan 4 \theta \tan 7 \theta\) then the general solution isCOMEDK 2018 Medium
- A tangent galvanometer has a reduction factor of \(1 \mathrm{~A}\) and it is placed with the plane of its coil perpendicular to the magnetic meridian. The deflection produced when a current of \(I A\) is passed through it isCOMEDK 2017 Medium
- The element with atomic number \(36\) belongs to \(\ldots \ldots .\) block in the periodic table.COMEDK 2013 Easy