Question:
A dice is thrown twice. If getting a number greater than four is considered a success, the variance of the probability distribution of the number of successes is
A dice is thrown twice. If getting a number greater than four is considered a success, the variance of the probability distribution of the number of successes is
Show Hint
For any binomial distribution problem, always identify the three core parameters first: \( n \) (total trials), \( p \) (success probability), and \( q \) (failure probability). Once you have these, finding statistical values like the mean (\( np \)) or variance (\( npq \)) becomes incredibly simple.
Updated On: Jun 8, 2026
- \( \frac{2}{9} \)
- \( \frac{2}{3} \)
- \( \frac{3}{4} \)
- \( \frac{4}{9} \)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
Repeated independent trials with fixed success probabilities follow a Binomial Distribution. The variance of a binomial distribution is given by the formula:
\[
\text{Variance} = n p q
\]
where \( n \) is the number of trials, \( p \) is the probability of success, and \( q = 1 - p \) is the probability of failure.
Step 1: Determining single-trial parameters.
A standard fair die has 6 outcomes: \( \{1, 2, 3, 4, 5, 6\} \). Success is defined as rolling a number strictly greater than 4, which includes only \( \{5, 6\} \) (2 outcomes). \[ p = \frac{2}{6} = \frac{1}{3} \] The probability of failure \( q \) is: \[ q = 1 - p = 1 - \frac{1}{3} = \frac{2}{3} \]
Step 2: Calculating the variance for the given number of trials.
The die is thrown twice, so the number of trials is \( n = 2 \). \[ \text{Variance} = n p q = 2 \times \frac{1}{3} \times \frac{2}{3} = \frac{4}{9} \]
Step 1: Determining single-trial parameters.
A standard fair die has 6 outcomes: \( \{1, 2, 3, 4, 5, 6\} \). Success is defined as rolling a number strictly greater than 4, which includes only \( \{5, 6\} \) (2 outcomes). \[ p = \frac{2}{6} = \frac{1}{3} \] The probability of failure \( q \) is: \[ q = 1 - p = 1 - \frac{1}{3} = \frac{2}{3} \]
Step 2: Calculating the variance for the given number of trials.
The die is thrown twice, so the number of trials is \( n = 2 \). \[ \text{Variance} = n p q = 2 \times \frac{1}{3} \times \frac{2}{3} = \frac{4}{9} \]
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 Distribution Questions
- The value of the constant \( c \), so that \( P(x) = c\left(\dfrac{2}{3}\right)^x,\, x = 1,2,3,\ldots \) is the probability distribution function of a discrete random variable \( X \), is:
- A random variable $X$ has the following probability distribution:
$X = x$: 0, 1, 2, 3, 4, 5
$P(X=x)$: $k$, $3k$, $5k$, $7k$, $9k$, $11k$
Then the value of $k$ is: - In a binomial distribution, the mean is 4 and the variance is 3. Then the number of trials $n$ is:
- Consider the random experiment of throwing a die and tossing a coin. Let \[ \{(a,b)\mid a\in\{H,T\},\ b\in\{1,2,\ldots,6\}\} \] denote the outcomes of the experiment. If $X$ is a random variable defined by \[ X(a,b)=b, \] then the variance of $X$ is
- If $X\sim B(n,p)$ is a binomial variate, $8p^2+15p-2=0$ and the product of the mean and variance of $X$ is $\dfrac78$, then $P(X=4)=$
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