Question:
Three unbiased coins are tossed. Then, the probability of getting at most two heads is:
Three unbiased coins are tossed. Then, the probability of getting at most two heads is:
Show Hint
“At most two heads” means all cases except getting three heads. Sometimes using the complement is faster.
Updated On: Jun 18, 2026
- \(\frac{3}{4}\)
- \(\frac{1}{4}\)
- \(\frac{3}{8}\)
- \(\frac{7}{8}\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Find total outcomes.
When three coins are tossed, total outcomes are \[ 2^3=8. \]
Step 2: Understand “at most two heads”.
At most two heads means number of heads can be \[ 0,\quad 1,\quad 2. \] The only case not allowed is getting \(3\) heads.
Step 3: Count favourable outcomes.
Total outcomes \(=8\).
Unfavourable outcome is \[ HHH. \] So, favourable outcomes are \[ 8-1=7. \]
Step 4: Find the probability.
\[ P(\text{at most two heads}) = \frac{7}{8}. \]
Step 5: Final conclusion.
Therefore, \[ \boxed{\frac{7}{8}} \]
When three coins are tossed, total outcomes are \[ 2^3=8. \]
Step 2: Understand “at most two heads”.
At most two heads means number of heads can be \[ 0,\quad 1,\quad 2. \] The only case not allowed is getting \(3\) heads.
Step 3: Count favourable outcomes.
Total outcomes \(=8\).
Unfavourable outcome is \[ HHH. \] So, favourable outcomes are \[ 8-1=7. \]
Step 4: Find the probability.
\[ P(\text{at most two heads}) = \frac{7}{8}. \]
Step 5: Final conclusion.
Therefore, \[ \boxed{\frac{7}{8}} \]
Was this answer helpful?
0
0
Top AP EAPCET Mathematics Questions
- $D = \left\{x\in\mathbb{R}: f\left(x\right) =\sqrt{\frac{x - \left|x\right|}{x - \left[x\right]}} \text{is defined} \right\}$ and $C$ be the range of the real function $g(x) = \frac{2x}{4 + x^{2}}$. Then $D \cap C$
- $f\left(x\right) = \frac{x}{e^{x}-1} + \frac{x}{2} + 2 \cos^{3} \frac{x}{2} $ on $R-\left\{0\right\} $ is
- Consider the following lists.
List-I List-II (A) $f(x) = \frac{|x+2|}{x+2} , x \ne -2 $ (I) $[\frac{1}{3} , 1 ]$ (B) $(x)=|[x]|,x \in [R$ (II) Z (C) $h(x) = |x - [x]| , x \in [R$ (III) W (D) $f(x) = \frac{1}{2 - \sin 3x} , x \in [R$ (IV) [0, 1) (V) { -1, 1} - If $[x]$ is the greatest integer less than or equal to $x$ and $|x|$ is the modulus of $x$. then the system of three equations $2x + 3 | y | + 5[z] = 0, x + |y| - 2[z] = 4, x + |y| + |z| = 1$ has
- Investigate the values of $\lambda$ and $\mu$ for the system $x+2 y+3 z=6, x+3 y+5 z=9$, $2 x+5 y+\lambda z=\mu$ and match the values in List - I with the items in List - II.
List I List II (A) $\lambda=8, \mu \neq 15$ 1. Infinitely many solutions (B) $\lambda \neq 8, \mu \in R$ 2. No solution (C) $\lambda=8, \mu=15$ 3. Unique solution
View More Questions
Top AP EAPCET Probability Questions
- If two numbers \(x\) and \(y\) are chosen one after the other at random with replacement from the set of numbers \( \{1, 2, 3, \ldots, 10\} \), then the probability that \( |x^2 - y^2| \) is divisible by 6 is:
- Bag A contains 3 white and 4 red balls, bag B contains 4 white and 5 red balls, and bag C contains 5 white and 6 red balls. If one ball is drawn at random from each of these three bags, then the probability of getting one white and two red balls is:
- Two persons A and B throw a pair of dice alternately until one of them gets the sum of the numbers appeared on the dice as 4 and the person who gets this result first is declared as the winner. If A starts the game, then the probability that B wins the game is:
- An urn contains 3 black and 5 red balls. If 3 balls are drawn at random from the urn, the mean of the probability distribution of the number of red balls drawn is:
- Let \(A\) and \(B\) be two independent events of a random experiment. If the probability that both \(A\) and \(B\) occur is \(\frac{1}{6}\) and the probability that neither of them occurs is \(\frac{1}{3}\), then the probability of occurrence of \(A\) is:
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions