Question:
A bag contains 3 black and 2 white balls. A ball is drawn at random and is put back in the bag along with one ball of the same colour. A ball is again drawn at random. What is the probability that it is white?
A bag contains 3 black and 2 white balls. A ball is drawn at random and is put back in the bag along with one ball of the same colour. A ball is again drawn at random. What is the probability that it is white?
Show Hint
Split problems into cases when outcomes affect future probabilities.
Updated On: Apr 30, 2026
- \(1/5\)
- \(2/5\)
- \(1/6\)
- \(1/12\)
- \(2/13\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
Use total probability considering both first-draw cases.
Step 1: Initial probabilities. \[ P(W_1)=\frac{2}{5}, P(B_1)=\frac{3}{5} \]
Step 2: Case 1: First draw is white. New balls: \[ 3B, 3W \] \[ P(W_2|W_1)=\frac{3}{6}=\frac{1}{2} \]
Step 3: Case 2: First draw is black. New balls: \[ 4B, 2W \] \[ P(W_2|B_1)=\frac{2}{6}=\frac{1}{3} \]
Step 4: Apply total probability. \[ P(W_2)=P(W_1)P(W_2|W_1)+P(B_1)P(W_2|B_1) \] \[ =\frac{2}{5}\cdot\frac{1}{2}+\frac{3}{5}\cdot\frac{1}{3} \] \[ =\frac{1}{5}+\frac{1}{5}=\frac{2}{5} \]
Step 1: Initial probabilities. \[ P(W_1)=\frac{2}{5}, P(B_1)=\frac{3}{5} \]
Step 2: Case 1: First draw is white. New balls: \[ 3B, 3W \] \[ P(W_2|W_1)=\frac{3}{6}=\frac{1}{2} \]
Step 3: Case 2: First draw is black. New balls: \[ 4B, 2W \] \[ P(W_2|B_1)=\frac{2}{6}=\frac{1}{3} \]
Step 4: Apply total probability. \[ P(W_2)=P(W_1)P(W_2|W_1)+P(B_1)P(W_2|B_1) \] \[ =\frac{2}{5}\cdot\frac{1}{2}+\frac{3}{5}\cdot\frac{1}{3} \] \[ =\frac{1}{5}+\frac{1}{5}=\frac{2}{5} \]
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM Multiplication Theorem on Probability Questions
- Find the locus of \( Z = x + iy \) satisfying \[ \frac{\text{Re}(z)}{2 + i} + \frac{\text{Im}(z)}{1 + 2i} = \frac{3}{1 - 2i} \]
- A box contains 4 red and 6 white marbles. Two successive draws of 3 balls are made without replacement. The probability that in first draw all the 3 balls are white and in second draw all the 3 balls are red, is
- A box contains 8 red balls, 10 white balls and 17 black balls. Two balls are drawn one by one without replacement. The probability that the first ball drawn is white and the second ball drawn is black, is
- If \( P(A)=0.4 \) and \( P(B|A)=0.9 \), then \( P(A \cap B) \) is equal to
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions