JEE Advanced · Mathematics · 32. Probability
Paragraph:
Let \(U_1\) and \(U_2\) be two urns such that \(U_1\) contains 3 white and 2 red balls and \(U_2\) contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from \(U_1\) and put into \(U_2\). However, if tail appears then 2 balls are drawn at random from \(U_1\) and put into \(U_2\). Now, 1 ball is drawn at random from \(U_2\).Question:
Given that the drawn ball from \(U_2\) is white, the probability that head appeared on the coin is
- A
\(\frac{17}{23}\)
- B
\(\frac{11}{23}\)
- C
\(\frac{15}{23}\)
- D
\(\frac{12}{23}\)
Answer & Solution
Correct Answer
(D)
\(\frac{12}{23}\)
Step-by-step Solution
Detailed explanation
\(P\) (head appeared/white from \(V_2\) )
\[
\begin{aligned}
& =P(H) \cdot \frac{\left\{\frac{{ }^3 C_1}{{ }^5 C_1} \times \frac{{ }^2 C_1}{{ }^2 C_1}+\frac{{ }^2 C_1}{{ }^5 C_1} \times \frac{{ }^1 C_1}{{ }^2 C_1}\right\}}{\frac{23}{30}} \\
& =\frac{1}{2} \frac{\left\{\frac{3}{5} \times 1+\frac{2}{5} \times \frac{1}{2}\right\}}{\frac{23}{30}}=\frac{12}{23} \\
&
\end{aligned}
\]
\[
\begin{aligned}
& =P(H) \cdot \frac{\left\{\frac{{ }^3 C_1}{{ }^5 C_1} \times \frac{{ }^2 C_1}{{ }^2 C_1}+\frac{{ }^2 C_1}{{ }^5 C_1} \times \frac{{ }^1 C_1}{{ }^2 C_1}\right\}}{\frac{23}{30}} \\
& =\frac{1}{2} \frac{\left\{\frac{3}{5} \times 1+\frac{2}{5} \times \frac{1}{2}\right\}}{\frac{23}{30}}=\frac{12}{23} \\
&
\end{aligned}
\]
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 Mathematics
- Let . Then the number of invertible matrices in isJEE Advanced 2023 Medium
- The value of is_____.JEE Advanced 2018 Easy
- Paragraph:
Let \(f:[0,1] \rightarrow \mathbb{R}\) (the set of all real numbers) be a function. Suppose the function \(f\) is twice differentiable, \(f(0)=f(1)=0\) and satisfies \(f^{\prime \prime}(x)-2 f^{\prime}(x)+f(x) \geq e^{x}, x \in[0,1] .\)
Question:
If the function \(\mathrm{e}^{-x} f(x)\) assumes its minimum in the interval \([0,1]\) at \(x=\frac{1}{4}\), which of the following is true?JEE Advanced 2013 Hard - Let denote the digit number where the first and the last digits are and the remaining digits are . Consider the sum . If , where and are natural numbers less than , then the value of isJEE Advanced 2023 Hard
- Suppose that all the terms of an arithmetic progression (A.P.) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is and the seventh terms lies in between and , then the common difference of this A.P. isJEE Advanced 2015 Easy
- Let \(A B C D\) be a quadrilateral with area 18 , with side \(A B\) parallel to the side \(C D\) and \(A B=2 C D\). Let \(A D\) be perpendicular to \(A B\) and \(C D\). If a circle is drawn inside the quadrilateral \(A B C D\) touching all the sides, then its radius isJEE Advanced 2007 Hard
More PYQs from JEE Advanced
- If is a twice differentiable function such that for all and thenJEE Advanced 2017 Easy
- Paragraph:
The circle \(x^2+y^2-8 x=0\) and hyperbola \(\frac{x^2}{9}-\frac{y^2}{4}=1\) intersect at the points \(A\) and \(B\).Question:
Equation of the circle with \(A B\) as its diameter isJEE Advanced 2010 Easy - Consider the kinetic data given in the following table for the reaction Product.
The rate of the reaction for and is found to be The value of is __________Ex
peri
ment No.\([\text A]\) \((\text{mol}\) \(\text{dm} ^{-3})\) \([\text B]\) \((\text{mol}\) \(\text{dm} ^{-3})\) \([\text C]\) \((\text{mol}\) \(\text{dm} ^{-3})\) Rate
of
reaction \((\text{mol}\) \(\text{dm} ^{-3}\) \(\text s^{-1})\)1 0.2 0.1 0.1 \(6.0 \times\) \(10^{-5}\) 2 0.2 0.2 0.1 \(6.0 \times \) \(10^{-5}\) 3 0.2 0.1 0.2 \(1.2 \times \) \(10^{-4}\) 4 0.3 0.1 0.1 \(9.0 \times \) \(10^{-5}\) JEE Advanced 2019 Medium - LIST-I contains reactions and LIST-II contains major products
Match each reaction in LIST-I with one or more products in LIST-II and choose the correct optionList - I List - II (A) 
(P) 
(B) 
(Q) 
(C) 
(R) 
(D) 
(S) 
(T) 
JEE Advanced 2018 Medium - Let and be positive real numbers. Suppose and are adjacent sides of a parallelogram Let and be the projection vectors of along and , respectively. If and if the area of the parallelogram is then which of the following statements is/are TRUE?JEE Advanced 2020 Medium
- Image of an object approaching a convex mirror of radius of curvature \(20 \mathrm{~m}\) along its optical axis is observed to move from \(\frac{25}{3} \mathrm{~m}\) to \(\frac{50}{7} \mathrm{~m}\) in \(30 \mathrm{~s}\). What is the speed of the object in \(\mathrm{km} \mathrm{h}^{-1}\) ?JEE Advanced 2010 Easy