Question:
For \( k = 1, 2, 3 \), the box \( B_k \) contains red balls and \( (k+1) \) white balls. Let \( P(B_1) = \frac{1}{2}, P(B_2) = \frac{1}{3}, P(B_3) = \frac{1}{6} \). A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it came from box \( B_2 \) is
For \( k = 1, 2, 3 \), the box \( B_k \) contains red balls and \( (k+1) \) white balls. Let \( P(B_1) = \frac{1}{2}, P(B_2) = \frac{1}{3}, P(B_3) = \frac{1}{6} \). A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it came from box \( B_2 \) is
Show Hint
When dealing with conditional probability, use Bayes' Theorem to reverse the probability and find the desired result.
Updated On: Mar 25, 2026
- \( \frac{35}{78} \)
- \( \frac{14}{39} \)
- \( \frac{10}{63} \)
- \( \frac{13}{78} \)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Use Bayes' Theorem.
Use Bayes' Theorem to calculate the probability. Bayes' Theorem states that: \[ P(B_2 | \text{Red}) = \frac{P(\text{Red} | B_2) P(B_2)}{P(\text{Red})} \]
Step 2: Conclusion.
The probability that the red ball came from box \( B_2 \) is \( \frac{14}{39} \). Final Answer: \[ \boxed{\frac{14}{39}} \]
Was this answer helpful?
0
0
Top BITSAT Mathematics Questions
- The solution of $\sin^{-1}\,x-\sin^{-1}\,2x=\pm\frac{\pi}{3}$ is
- If one root of the quadratic equation $a x^{2}+b x+c=0$ is equal to $n^{\text {th }}$ power of the other root, then the value of: $a^{\frac{n}{n-1}} C^{\frac{1}{n-1}}+c^{\frac{n}{n-1}} a^{\frac{1}{n-1}}$ is equal to
- $(x -1) (x^2 - 5x + 7) < (x -,1),$ then $x$ belongs to
- An ellipse has $OB$ as semi-minor axis, $F$ and $F$ are its foci and the $\angle FBF$, is a right angle. Then, the eccentricity of the ellipse is
- $2^{1/4}. 2^{2/8}. 2^{3/16}. 2^{4/32}......\infty$ is equal to-
View More Questions
Top BITSAT Bayes' Theorem Questions
- If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is :
- For $k=1,2,3$ the box $Bk$ contains $k$ red balls and $(k+1)$ white balls. Let $P\left(B_{1}\right)=\frac{1}{2}, P\left(B_{2}\right)=\frac{1}{3}=\frac{1}{3}$ and $P\left(B_{3}\right)=\frac{1}{6} .$ A box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box $B_{2}$, is
- Let $A$ and $B$ are two events and $P \left( A '\right)=0.3, P ( B )=0.4, P \left( A \cap B '\right)=0.5$, then $P ( A \cup B)$ is.
- An urn contains five balls. Two balls are drawn and found to be white. The probability that all the balls are white is
Top BITSAT Questions
- Two point charges $-q$ and $+ q$ are located at point's $(0, 0, - a)$ and, $(0, 0, a)$ respectively. The electric potential at a point $(0, 9, z)$, where $z > a$ is
- Which of the following must be known in order to determine the power output of an automobile?
- A large drop of oil (density $0.8 \,g / cm ^{3}$ and viscosity $\eta_{0}$ ) floats up through a column of another liquid (density $1.2\, g / cm ^{3}$ and viscosity $\eta_{L}$ ). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on :
- A body is projected vertically upwards at time $ t = 0$ and it is seen at a height $H$ at time $t_1$ and $t_2$ second during its flight. The maximum height attained is ($g$ is acceleration due to gravity)
- At what point of a projectile motion, acceleration and velocity are perpendicular to each other ?
View More Questions