TS EAMCET · Maths · Probability
If \(A\) and \(B\) are mutually exclusive events with \(P(B) \neq 1\), then \(P(A \mid \bar{B})\) is equal to (Here \(\bar{B}\) is the complement of the event \(B\) )
- A \(\frac{1}{P(B)}\)
- B \(\frac{1}{1-P(B)}\)
- C \(\frac{P(A)}{P(B)}\)
- D \(\frac{P(A)}{1-P(B)}\)
Answer & Solution
Correct Answer
(D) \(\frac{P(A)}{1-P(B)}\)
Step-by-step Solution
Detailed explanation
Given, \(A\) and \(B\) are mutually exclusive events So, \((A \cap B)=\phi\). Now, \(\begin{aligned} P(A \mid \bar{B}) & =\frac{P(A \cap \bar{B})}{P(\bar{B})}=\frac{P(A)-P(A \cap B)}{P(\bar{B})} \\ & =\frac{P(A)}{1-P(B)}\end{aligned}\)
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
- Let \(a, b \in \mathbf{R}\) and the roots \(\alpha, \beta\) of the equation \(z^2+a z+b=0\) be complex. If the origin, \(\alpha\) and \(\beta\) represent the vertices of an equilateral triangle on the Argand plane, thenTS EAMCET 2020 Medium
- The foot of the perpendicular drawn from the point \((1,1,1)\) to the plane \(\pi_1\) is \((1,3,5)\). If \((2,2,-1),(3,4,2),(3,3,0)\) are three points on the plane \(\pi_2\), then the angle between the planes \(\pi_1\) and \(\pi_2\) isTS EAMCET 2020 Hard
- If the mean of the discrete distribution 8,9 , \(6,5, x, 4,6,5\) is 6 , then its standard deviation (nearest to two decimal places) isTS EAMCET 2020 Easy
- \(\int \frac{3^x}{\sqrt{9^x-1}} d x=\)TS EAMCET 2018 Easy
- If two cards are drawn at random simultaneously from a well shuffled pack of 52 playing cards, then the probability of getting a card having a composite number and a card having a number which is a multiple of 3 isTS EAMCET 2024 Hard
- If and , thenTS EAMCET 2018 Medium
More PYQs from TS EAMCET
- A block is in simple harmonic motion (S.H.M) on the end of the spring with position given by \(x=(5) \cos \left(\omega t+\frac{\pi}{4}\right)\) If the total mechanical energy used is 100 J to achieve maximum displacement, then the potential energy at time t = 0 isTS EAMCET 2022 Medium
- If \(P=\left|\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right|\) is the adjoint of a \(3 \times 3\) matrix \(A\) and \(\operatorname{det}(A)=4\), then \(\alpha\) is equal toTS EAMCET 2021 Easy
- Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be defined by \(f(x)=5^{-|x|}+\operatorname{sgn}\left(5^{-x}\right)\), where \(\operatorname{sgn} x\) denotes signum function of \(x\). Then \(f\) isTS EAMCET 2025 Medium
- Identify the pair that is not is ostructural.TS EAMCET 2018 Easy
- An infinite long wire lying along the \(Y\)-axis, is carrying a current \(I\) as shown in the figure. The magnetic flux through a circular loop of radius \(R\) in the \(x y\)-plane is [assume, \(\mu_0=\) magnetic in free space permeability]
TS EAMCET 2020 Easy - Which element does not exist in elemental state in the earth's crust?TS EAMCET 2020 Easy