JEE Mains · Maths · STD 11 - 14. probability
Let \(X\) be a set containing \(10\) elements and \(P(X)\) be its power set. If \(A\) and \(B\) are picked up at random from \(P(X),\) with replacement, then the probability that \(A\) and \(B\) have equal number elements, is
- A \(\frac{{\left( {{2^{10}} - 1} \right)}}{{{2^{10}}}}\)
- B \(\frac{{^{20}{C_{10}}}}{{{2^{10}}}}\)
- C \(\frac{{\left( {{2^{10}} - 1} \right)}}{{{2^{20}}}}\)
- D \(\frac{{^{20}{C_{10}}}}{{{2^{20}}}}\)
Answer & Solution
Correct Answer
(D) \(\frac{{^{20}{C_{10}}}}{{{2^{20}}}}\)
Step-by-step Solution
Detailed explanation
Required porbability is \(\frac{{{{\left( {^{10}{C_0}} \right)}^2} + {{\left( {^{10}{C_1}} \right)}^2} + {{\left( {^{10}{C_2}} \right)}^2} + ...... + {{\left( {^{10}{C_{10}}} \right)}^2}}}{{{2^{10}}}}\) \( = \frac{{{\,^{20}}{C_{10}}}}{{{2^{20}}}}\)
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 one of the diameters of the circle \(x^{2}+y^{2}-2 \sqrt{2} x\) \(-6 \sqrt{2} y+14=0\) is a chord of the circle \((x-2 \sqrt{2})^{2}\) \(+(y-2 \sqrt{2})^{2}=r^{2}\), then the value of \(r^{2}\) is equal toJEE Mains 2022 Hard
- If the equation of the plane passing through the line of intersection of the planes \(2 x-7 y+4 z-3=0,3 x-5 y+4 z+11=0\) and the point \((-2,1,3)\) is \(a x+b y+c z-7=0,\) then the value of \(2 a+b+c-7\) isJEE Mains 2021 Hard
- Let \(S=2+\frac{6}{7}+\frac{12}{7^{2}}+\frac{20}{7^{3}}+\frac{30}{7^{4}}+\ldots . .\) then \(4 S\) is equal toJEE Mains 2022 Hard
- Let \(\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=3 \hat{i}+2 \hat{j}-\hat{k}, \vec{c}=\lambda \hat{j}+\mu \hat{k}\) and \(\hat{d}\) be a unit vector such that \(\overrightarrow{\mathrm{a}} \times \hat{\mathrm{d}}=\overrightarrow{\mathrm{b}} \times \hat{\mathrm{d}}\) and \(\overrightarrow{\mathrm{c}} \cdot \hat{\mathrm{d}}=1\), If \(\vec{c}\) is perpendicular to \(\vec{a}\), then \(|3 \lambda \hat{d}+\mu \overrightarrow{\mathrm{c}}|^2\) is equal to _______ .JEE Mains 2025 Medium
- Let \(f\left( x \right) = x\left| x \right|\,,\,g\left( x \right) = \sin \,x\) and \(h\left( x \right) = \left( {gof} \right)\left( x \right)\). ThenJEE Mains 2014 Hard
- The area of the region, inside the ellipse \( x^{2}+4y^{2}=4 \) and outside the region bounded by the curves \( y=|x|-1 \) and \( y=1-|x| \), is:JEE Mains 2026 Medium
More PYQs from JEE Mains
- Let the foci of a hyperbola be \((1,14)\) and \((1,-12)\). If it passes through the point \((1,6)\), then the length of its latus-rectum is :JEE Mains 2025 Easy
- Let \(O\) be the origin and \(OP\) and \(OQ\) be the tangents to the circle \(x^2+y^2-6 x+4 y+8=0\) at the point \(P\) and \(Q\) on it. If the circumcircle of the triangle OPQ passes through the point \(\left(\alpha, \frac{1}{2}\right)\), then a value of \(\alpha\) isJEE Mains 2023 Hard
- If \(y=y(x)\) is the solution curve of the differential equation \(\left(x^2-4\right) d y-\left(y^2-3 y\right) d x=0\), \(x>2, y(4)=\frac{3}{2}\) and the slope of the curve is never zero, then the value of \(y(10)\) equals :JEE Mains 2024 Hard
- Let \(f ( x )= |x -2|\) and \(g ( x )= f ( f ( x )), x \in[0,4]\) Then \(\int \limits_{0}^{3}(g(x)-f(x)) d x\) is equal toJEE Mains 2020 Medium
- Let the line of the shortest distance between the lines \(L_1: \vec{r}=(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k})\) and \(L_2: \vec{r}=(4 \hat{i}+5 \hat{j}+6 \hat{k})+\mu(\hat{i}+\hat{j}-\hat{k})\) intersect \(\mathrm{L}_1\) and \(\mathrm{L}_2\) at \(\mathrm{P}\) and \(\mathrm{Q}\) respectively. If \((\alpha, \beta, \gamma)\) is the midpoint of the line segment \(PQ\), then \(2(\alpha+\beta+\gamma)\) is equal to ...........JEE Mains 2024 Hard
- Let \({f_k}\left( x \right) = \frac{1}{k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)\;,x \in R\) and \(k \ge 1\), then \({f_4}\left( x \right) - {f_6}\left( x \right)\) is equal toJEE Mains 2014 Hard