Find the probability distribution of the number of tails in the simultaneous tosses of three coins.
(N/A) When three coins are tossed simultaneously,the sample space is $S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$.
Let $X$ represent the number of tails.
It can be seen that $X$ can take the values $0, 1, 2,$ or $3$.
$P(X=0) = P(HHH) = \frac{1}{8}$
$P(X=1) = P(HHT) + P(HTH) + P(THH) = \frac{1}{8} + \frac{1}{8} + \frac{1}{8} = \frac{3}{8}$
$P(X=2) = P(HTT) + P(THT) + P(TTH) = \frac{1}{8} + \frac{1}{8} + \frac{1}{8} = \frac{3}{8}$
$P(X=3) = P(TTT) = \frac{1}{8}$
Thus,the probability distribution is as follows:
Let $X$ represent the number of tails.
It can be seen that $X$ can take the values $0, 1, 2,$ or $3$.
$P(X=0) = P(HHH) = \frac{1}{8}$
$P(X=1) = P(HHT) + P(HTH) + P(THH) = \frac{1}{8} + \frac{1}{8} + \frac{1}{8} = \frac{3}{8}$
$P(X=2) = P(HTT) + P(THT) + P(TTH) = \frac{1}{8} + \frac{1}{8} + \frac{1}{8} = \frac{3}{8}$
$P(X=3) = P(TTT) = \frac{1}{8}$
Thus,the probability distribution is as follows:
| $X$ | $0$ | $1$ | $2$ | $3$ |
| $P(X)$ | $\frac{1}{8}$ | $\frac{3}{8}$ | $\frac{3}{8}$ | $\frac{1}{8}$ |
Explore More
Similar Questions
If the probability distribution is given by $P(x) = C \binom{4}{x}$ for $x = 0, 1, 2, 3, 4$,then find the value of $C$.
$A$ random variable $X$ has the probability distribution given below. Its variance is:
$X$ $1$ $2$ $3$ $4$ $5$ $P(X=x)$ $K$ $2K$ $3K$ $2K$ $K$
| $X$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $P(X=x)$ | $K$ | $2K$ | $3K$ | $2K$ | $K$ |
If a random variable $X$ has the following probability distribution values,then $P(X \geq 6)$ has the value:
$X$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $P(X)$ $0$ $k$ $2k$ $2k$ $3k$ $k^2$ $2k^2$ $7k^2 + k$
| $X$ | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ |
| $P(X)$ | $0$ | $k$ | $2k$ | $2k$ | $3k$ | $k^2$ | $2k^2$ | $7k^2 + k$ |
Let $X$ be a random variable with the following probability distribution:
$x$ $-2$ $-1$ $3$ $4$ $6$ $P(X=x)$ $\frac{1}{5}$ $a$ $\frac{1}{3}$ $\frac{1}{5}$ $b$
If the mean of $X$ is $2.3$ and the variance of $X$ is $\sigma^{2}$,then $100 \sigma^{2}$ is equal to:
| $x$ | $-2$ | $-1$ | $3$ | $4$ | $6$ |
| $P(X=x)$ | $\frac{1}{5}$ | $a$ | $\frac{1}{3}$ | $\frac{1}{5}$ | $b$ |
If the mean of $X$ is $2.3$ and the variance of $X$ is $\sigma^{2}$,then $100 \sigma^{2}$ is equal to:
DifficultJEE MAIN 2021
View SolutionIf two dice are thrown and if $X$ denotes the sum of the numbers that show up on the faces of the dice, then the mean of the random variable $X$ is
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo