JEE Mains · Maths · STD 12 - 13. probability
Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is \(\frac{m}{n}\), where \(\operatorname{gcd}(m, n)=1\), then \(m+n\) is equal to :
- A \(4\)
- B \(14\)
- C \(13\)
- D \(11\)
Answer & Solution
Correct Answer
(B) \(14\)
Step-by-step Solution
Detailed explanation
Bag contains 4 white and 6 black balls \(A\) : first ball selected is black \(B\) : Second ball is also black…
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 \(x\) and \(y\) be distinct integers where \(1 \leq x \leq 25\) and \(1 \leq y \leq 25\). Then, the number of ways of choosing \(x\) and \(y\), such that \(x + y\) is divisible by \(5\) , is \(.........\).JEE Mains 2023 Hard
- If the maximum distance of normal to the ellipse \(\frac{x^2}{4}+\frac{y^2}{b^2}=1, b < 2\), from the origin is \(1\) , then the eccentricity of the ellipse is:JEE Mains 2023 Hard
- A bird is sitting on the top of a vertical pole \(20\, m\) high and its elevation from a point \(O\) on the ground is \(45^o \) . It flies off horizontally straight away from the point \(O\). After one second, the elevation of the bird from \(O\) is reduced to \(30^o \) . Then the speed (in \(m/s\)) of the bird isJEE Mains 2014 Hard
- If \(y=\tan ^{-1}\left(\sec x^{3}-\tan x^{3}\right) \cdot \frac{\pi}{2} < x^{3} < \frac{3 \pi}{2}\), thenJEE Mains 2022 Hard
- If \(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\ldots+\frac{1}{\sqrt{99}+\sqrt{100}}=m\) and \(\frac{1}{1 \cdot 2}+\frac{1}{2 \cdot 3}+\ldots+\frac{1}{99 \cdot 100}=\mathrm{n}\), then the point \((\mathrm{m}, \mathrm{n})\) lies on the lineJEE Mains 2024 Hard
- Two vertices of a triangle \(\mathrm{ABC}\) are \(\mathrm{A}(3,-1)\) and \(\mathrm{B}(-2,3)\), and its orthocentre is \(\mathrm{P}(1,1)\). If the coordinates of the point \(\mathrm{C}\) are \((\alpha, \beta)\) and the centre of the circle circumscribing the triangle \(\mathrm{PAB}\) is \((h, k)\), then the value of \((\alpha+\beta)+2(h+k)\) equals :JEE Mains 2024 Hard
More PYQs from JEE Mains
- The interval in which the function \(\mathrm{f}(\mathrm{x})=\mathrm{x}^{\mathrm{x}}, \mathrm{x}>0\), is strictly increasing isJEE Mains 2024 Medium
- Let the line \(x+y=1\) meet the axes of \(x\) and \(y\) at A and B, respectively. A right angled triangle AMN is inscribed in the triangle OAB , where O is the origin and the points M and N lie on the lines \(O B\) and \(A B\), respectively. If the area of the triangle \(A M N\) is \(\frac{4}{9}\) of the area of the triangle \(O A B\) and AN : NB \(=\lambda: 1\), then the sum of all possible value(s) of is \(\lambda\) :JEE Mains 2025 Hard
- The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a dictionary. The rank of the word "UDAYPUR" is:JEE Mains 2026 Hard
- If \(f\left( {\frac{{3x - 4}}{{3x + 4}}} \right) = x + 2,\,x \ne -\frac{4}{3}\) , and \(\int {f\left( x \right)dx = A\,\log \left| {1 - x} \right| + Bx + C} \) , then the ordered pair \((A,B) \) is equal to : (where \(C\) is a constant of integration)JEE Mains 2017 Hard
- The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be \(45^{\circ} .\) After walking a distance of \(80\) meters towards the top, up a slope inclined at an angle of \(30^{\circ}\) to the horizontal plane, the angle of elevation of the top of the hill becomes \(75^{\circ} .\) Then the height of the hill (in meters) isJEE Mains 2020 Hard
- The eccentricity of an ellipse \(E\) with centre at the origin \(O\) is \(\dfrac{\sqrt{3}}{2}\) and its directrices are \(x = \pm \dfrac{4\sqrt{6}}{3}\). Let \(H: \dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1\) be a hyperbola whose eccentricity is equal to the length of semi-major axis of \(E\), and whose length of latus rectum is equal to the length of minor axis of \(E\). Then the distance between the foci of \(H\) is :JEE Mains 2026 Hard