AP EAMCET · Maths · Probability
\(A\) and \(B\) are two events such that \(P(A)=0.58\), \(P(B)=0.32\) and \(P(A \cap B)=0.28\). Then the probability that neither \(A\) nor \(B\) occurs is
- A 0.38
- B 0.62
- C 0.72
- D 0.9
Answer & Solution
Correct Answer
(A) 0.38
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & P(\bar{A} \cap \bar{B})=P(A \cup B)=1-P(A \cup B) \\ & =1-\{P(A)+P(B)-P(A \cap B)\} \\ & =1-\{0.58+0.32-0.28\}=1-0.62=0.38\end{aligned}\)
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
- If \((a, b)\) is the centroid of the triangle formed by the lines \(4 x^2-17 x y+4 y^2=0\) and \(x+y-5=0\) and \(c\) is the numerical value of the area of the triangle, then \(a+b+c=\)AP EAMCET 2018 Medium
- A shopkeeper buys a particular type of electric bulbs from three manufactures \(M_1, M_2\) and \(M_3\). He buys \(25 \%\) of his requirement from \(M_1, 45 \%\) from \(M_2\), and \(30 \%\) from \(M_3\). Based on past experience he found that \(2 \%\) of type \(\mathrm{M}_3\) bulbs are defective, where as only \(1 \%\) of type \(M_1\) and type \(\mathrm{M}_2\) are detective. If a bulb chosen by him at random is defective, then the probability that it was of type \(M_3\) isAP EAMCET 2023 Easy
- The equation of the line passing through the point of intersection of the lines \(2 x+3 y+6=0,3 x-y-13=0\) and parallel to the line \(3 x-4 y+5=0\) isAP EAMCET 2018 Easy
- In \(\triangle A B C, \angle A=90^{\circ}\) and co-ordinates of points \(B\) and \(C\) are \((2,-4)\) and \((1,5)\). Then the equation of the circumcircle of \(\triangle A B C\) isAP EAMCET 2020 Medium
- The locus of the complex number Z such that \(\arg \left(\frac{Z-1}{Z+1}\right)=\frac{\pi}{4}\) isAP EAMCET 2024 Easy
- Lagrange's mean value theorem is not applicable in \([0,1]\) to the functionAP EAMCET 2017 Medium
More PYQs from AP EAMCET
- The density of methane is maximum under which conditions?AP EAMCET 2022 Medium
- If the equation of the tangent of the hyperbola \(5 x^2-9 y^2-20 x-18 y-34=0\) which makes an angle \(45^{\circ}\) with the positive X -axis in positive direction is \(x+b y+c=0\) then \(b^2+c^2=\)AP EAMCET 2025 Hard
- The equilibrium concentrations of \(\mathrm{N}_2, \mathrm{H}_2\) and \(\mathrm{NH}_3\) in the formation of \(\mathrm{NH}_3\) at \(500 \mathrm{~K}\) are \(1.25 \times 10^{-2} \mathrm{M}, 4.0 \times 10^{-2} \mathrm{M}\) and \(1.6 \times 10^{-2} \mathrm{M}\) respectively. The equilibrium constant \(\mathrm{K}_{\mathrm{p}}\) at the same temperature isAP EAMCET 2018 Easy
- The equation of the ellipse having a vertex at \((6,1)\), a focus at \((4,1)\) and the eccentricity \(\frac{3}{5}\) isAP EAMCET 2018 Easy
- Let \(\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}\) be two vectors. If \(A_1\) is the area of the quadrilateral having \(\vec{a}, \vec{b}\) as its diagonals and \(A_2\) is the area of the parallelogram having \(\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}\) as its two adjacent sides, then \(\mathrm{A}_1 \cdot \mathrm{A}_2=\)AP EAMCET 2023 Easy
- A transverse wave is represented by the equation \(y=2 \sin (30 t-40 x)\) and the measurements of distances are in meters, then the velocity of propagation isAP EAMCET 2015 Easy