AP EAMCET · Maths · Probability
On every evening, a student either watches TV or reads a book. The probability of watching TV is \(\frac{4}{5}\). If he watches TV, the probability that he will fall asleep is \(\frac{3}{4}\) and it is \(\frac{1}{4}\) when he reads a book. If the student is found to be asleep on an evening, the probability that he watched the TV is
- A \(\frac{11}{13}\)
- B \(\frac{12}{13}\)
- C \(\frac{2}{13}\)
- D \(\frac{4}{13}\)
Answer & Solution
Correct Answer
(B) \(\frac{12}{13}\)
Step-by-step Solution
Detailed explanation
\(P(A) = P(A|T)P(T) + P(A|R)P(R)\) \(P(A) = \left(\frac{3}{4}\right)\left(\frac{4}{5}\right) + \left(1 - \frac{4}{5}\right)\left(\frac{1}{4}\right)\) \(P(A) = \frac{12}{20} + \frac{1}{20} = \frac{13}{20}\) \(P(T|A) = \frac{P(A|T)P(T)}{P(A)}\)…
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 mid-point of a chord of the ellipse \(x^2+4 y^2-2 x+20 y=0 \quad\) is \((2,-4)\). The equation of the chord isAP EAMCET 2013 Medium
- If \(\frac{3 x+2}{(x+1)\left(2 x^2+3\right)}=\frac{A}{x+1}+\frac{B x+C}{2 x^2+3}\), then \(A+C-B\) is equal to :AP EAMCET 2006 Easy
- If \(\mathrm{A}\) and \(\mathrm{B}\) are two events of a random experiment such that \(P(A \cup B)=0.65\) and \(P(A \cap B)=0.15\), then \(\mathrm{P}(\overline{\mathrm{A}})+\mathrm{P}(\overline{\mathrm{B}})=\)AP EAMCET 2023 Easy
- The value of \(\cos \left(\frac{7 \pi}{12}\right)\) isAP EAMCET 2022 Easy
- If the equation of the pair of lines passing through \((1,1)\) and perpendicular to the pair of lines \(2 x^2+x y-y^2-x+2 y-1=0\) is \(a x^2+2 h x y+b y^2+2 g x+3 y=0\), then \(\frac{b}{a}=\)AP EAMCET 2025 Hard
- An ellipse has 6 and 2 as length of major and minor axes respectively. If the centre is at \((5,6)\) and the major axis is along \(x-y+1=0\), then the ellipse isAP EAMCET 2022 Easy
More PYQs from AP EAMCET
- The reaction
\(\mathrm{Ar}_2 \stackrel{\ominus}{\mathrm{C}} \stackrel{\oplus}{\mathrm{Cl}}+\mathrm{Cu}+\mathrm{HCl} \longrightarrow \mathrm{ArCl}+\mathrm{N}_2+\mathrm{CuCl}\)
is known asAP EAMCET 2019 Easy - If \(\int_0^\pi \frac{d x}{1+2 \sin ^2 x}=k\), then greatest integer less than or equal to \(k\) isAP EAMCET 2022 Medium
- A motor can pump 7560 kg of water per hour from a well of depth 100 m. If the efficiency of the pump is \(70 \%\), then power of the pump is (Acceleration due to gravity \(=10 \mathrm{~m} \mathrm{~s}^{-2}\) )AP EAMCET 2025 Medium
- If the sides \(a, b, c\) of the triangle \(A B C\) are in harmonic progression, then \(\operatorname{cosec}^2 \mathrm{~A} / 2, \operatorname{cosec}^2 \mathrm{~B} / 2, \operatorname{cosec}^2 \mathrm{C} / 2\) are inAP EAMCET 2025 Medium
- If the lines \(x^2+2 x y-35 y^2-4 x+44 y-12=0\) and \(5 x+k y-8=0\) are concurrent, then \(k\) equalsAP EAMCET 2021 Medium
- If , then is equal toAP EAMCET 2021 Medium