JEE Mains · Maths · STD 12 - 13. probability
There are three bags \(X\), \(Y\) and \(Z\). Bag \(X\) contains \(5\) one-rupee coins and \(4\) five-rupee coins; Bag \(\mathrm{Y}\) contains \(4\) one-rupee coins and \(5\) five-rupee coins and Bag \(\mathrm{Z}\) contains \(3\) one-rupee coins and \(6\) five-rupee coins. A bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability, that it came from bag \(\mathrm{Y}\), is :
- A \(\frac{1}{3}\)
- B \(\frac{1}{2}\)
- C \(\frac{1}{4}\)
- D \(\frac{5}{12}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
\(X\ \&\ Y\ \&\ Z\) 5 one \(\&\ 4\) five 4 one \(\&\ 5\) five 3 one \(\&\ 6\) five \(P=\frac{4 / 9}{5 / 9+4 / 9+3 / 9}=\frac{4}{12}=\frac{1}{3}\)
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 the area enclosed between the curves \(|y|=1-x^2\) and \(x^2+y^2=1\) be \(\alpha\). If \(9 \alpha=\beta \pi+\gamma ; \beta, \gamma\) are integers, then the value of \(|\beta-\gamma|\) equals.JEE Mains 2025 Medium
- The number of terms common to the two A.P.'s \(3,7,11, \ldots ., 407\) and \(2,9,16, \ldots . .709\) isJEE Mains 2020 Hard
- For the system of linear equations \(2 x-y+3 z=5\) \(3 x+2 y-z=7\) \(4 x+5 y+\alpha z=\beta\) Which of the following is NOT correct ?JEE Mains 2023 Hard
- Let \(\quad S=\left\{z \in C-\{i, 2 i\}: \frac{z^2+8 i z-15}{z^2-3 i z-2} \in R \right\}\). \(\alpha-\frac{13}{11} i \in S , \alpha \in R -\{0\}\), then \(242 \alpha^2\) is equal toJEE Mains 2023 Hard
- If the tangent at a point on the ellipse \(\frac{{{x^2}}}{{27}} + \frac{{{y^2}}}{3} = 1\) meets the coordinate axes at \(A\) and \(B,\) and \(O\) is the origin, then the minimum area (in sq. units) of the triangle \(OAB\) isJEE Mains 2016 Hard
- Choose the incorrect statement about the two circles whose equations are given below \(x^{2}+y^{2}-10 x-10 y+41=0\) and \(x^{2}+y^{2}-16 x-10 y+80=0\)JEE Mains 2021 Medium
More PYQs from JEE Mains
- The length of the projection of the line segment joining the point \(\left( {5, - 1,4} \right)\) and \(\left( {4, - 1,3} \right)\) on the plane \(x + y + z = 7\) is :
JEE Mains 2018 Hard - Considering only the principal values of the inverse trigonometric functions, the domain of the function \(f(x)=\cos ^{-1}\left(\frac{x^{2}-4 x+2}{x^{2}+3}\right)\) is.JEE Mains 2022 Medium
- Let \(\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\mathrm{k}, \overrightarrow{\mathrm{b}}=3(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\mathrm{k})\). Let \(\overrightarrow{\mathrm{c}}\) be the vector such that \(\vec{a} \times \vec{c}=\vec{b}\) and \(\vec{a} \cdot \vec{c}=3\). Then \(\overrightarrow{\mathrm{a}} \cdot((\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{b}})-\overrightarrow{\mathrm{b}}-\overrightarrow{\mathrm{c}})\) is equal to :JEE Mains 2024 Hard
- Let \(r\) be the radius of the circle, which touches x -axis at point \((\mathrm{a}, 0), \mathrm{a} \lt 0\) and the parabola \(\mathrm{y}^2=9 \mathrm{x}\) at the point \((4,6)\). Then \(r\) is equal to ________JEE Mains 2025 Medium
- The equation of a tangent to the parabola, \(x^2 = 8y,\) which makes an angle \(\theta \) with the positive direction of \(x-\) axis, isJEE Mains 2019 Hard
- Let \(f:[0, \infty) \rightarrow[0,3]\) be a function defined by \(f(x)=\max \{\sin t: 0 \leq t \leq x\}, \quad 0 \leq x \leq \pi\) \(\quad \quad \quad \quad \quad \quad 2+\cos x,\quad \quad \quad \quad x>\pi\) Then which of the following is true?JEE Mains 2021 Hard