Question:
A bag contains \((2n+1)\) coins. It is known that \(n\) of these coins have a head on both sides, whereas the remaining \((n+1)\) coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is \(\frac{31}{42}\), then \(n\) is equal to
A bag contains \((2n+1)\) coins. It is known that \(n\) of these coins have a head on both sides, whereas the remaining \((n+1)\) coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is \(\frac{31}{42}\), then \(n\) is equal to
Show Hint
Use total probability = sum of (probability × conditional probability).
Updated On: Mar 23, 2026
- \(10\)
- \(11\)
- \(12\)
- \(13\)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Probability of choosing a double-headed coin: \[ \frac{n}{2n+1} \]
Step 2: Probability of choosing a fair coin: \[ \frac{n+1}{2n+1} \]
Step 3: Total probability of head: \[ P(H)=\frac{n}{2n+1}\cdot1+\frac{n+1}{2n+1}\cdot\frac12 =\frac{3n+1}{2(2n+1)} \]
Step 4: Given: \[ \frac{3n+1}{2(2n+1)}=\frac{31}{42} \Rightarrow n=11 \]
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 Probability Questions
- A bag contains $3$ white and $5$ black balls. One ball is drawn at random. Then the probability that it is white is:
- A bag contains $3$ red and $3$ white balls. Two balls are drawn one by one. The probability that they are of different colours is.
- A bag contains $2n$ coins out of which $n-1$ are unfair with heads on both sides and the remaining are fair. One coin is picked from the bag at random and tossed. If the probability that head falls in the toss is $\frac{41}{56}$, then the number of unfair coins in the bag is
- The probability of getting $10$ in a single throw of three fair dice is :
- Let $S$ be a set containing n elements and we select two subsets $A$ and $D$ of S at random, then the probability that $A \cup B = S$ and $A \cap B = \phi$ is:
View More Questions
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