(B) The number of floors available to leave, excluding the ground floor, is $6$. Each of the $5$ persons can choose any of the $6$ floors independentl

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(B) The number of floors available to leave, excluding the ground floor, is $6$. Each of the $5$ persons can choose any of the $6$ floors independently. Therefore, the total number of ways the $5$ persons can leave is $6^5$. The number of ways the $5$ persons can leave at $5$ different floors is given by the permutation formula $^6P_5$. $^6P_5 = \frac{6!}{(6-5)!} = 6 \times 5 \times 4 \times 3 \times 2 = 720$. The total number of outcomes is $6^5 = 7776$. The probability is $\frac{^6P_5}{6^5} = \frac{720}{7776}$. Simplifying the fraction: $\frac{720}{7776} = \frac{5}{54}$.

Class 12 Mathematics Probability Probability distribution

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$5$ persons entered a lift cabin on the ground floor of a $7$-floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first. The probability of all the $5$ persons leaving the cabin at different floors is

TS EAMCET 2018 All TS EAMCET

A
$\frac{360}{2401}$
B
$\frac{5}{54}$
C
$\frac{5}{18}$
D
$\frac{5!}{7!}$

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Probability

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Probability distribution

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The probability distribution of a discrete random variable $X$ is given below:
$X = x$ $-1$ $0$ $1$ $2$
$P(X = x)$ $\frac{1}{3}$ $\frac{1}{6}$ $\frac{1}{6}$ $\frac{1}{3}$

Then the value of $6 \Sigma(x^2) P(X=x) - \operatorname{var}(X) =$ ?

$X = x$	$-1$	$0$	$1$	$2$
$P(X = x)$	$\frac{1}{3}$	$\frac{1}{6}$	$\frac{1}{6}$	$\frac{1}{3}$

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If a random variable $X$ has the following probability distribution values,then $P(X \geq 6)$ has the value:
$X$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$
$P(X)$ $0$ $k$ $2k$ $2k$ $3k$ $k^2$ $2k^2$ $7k^2 + k$

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Which of the following cannot be a valid assignment of probabilities for outcomes of sample space $S = \{\omega_{1}, \omega_{2}, \omega_{3}, \omega_{4}, \omega_{5}, \omega_{6}, \omega_{7}\}$?
Outcome $\omega_{1}$ $\omega_{2}$ $\omega_{3}$ $\omega_{4}$ $\omega_{5}$ $\omega_{6}$ $\omega_{7}$
Probability $-0.1$ $0.2$ $0.3$ $0.4$ $-0.2$ $0.1$ $0.3$

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$A$ discrete random variable $X$ takes values $10, 20, 30,$ and $40$,with probabilities $0.3, 0.3, 0.2,$ and $0.2$ respectively. Then the expected value of $X$ is

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The range of a random variable $X$ is $\{0, 1, 2\}$. If $P(X = 0) = 3c^3$, $P(X = 1) = 4c - 10c^2$, and $P(X = 2) = 5c - 1$, then find $P(0 < X \le 2)$.

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$X$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(X)$	$0$	$k$	$2k$	$2k$	$3k$	$k^2$	$2k^2$	$7k^2 + k$

Outcome	$\omega_{1}$	$\omega_{2}$	$\omega_{3}$	$\omega_{4}$	$\omega_{5}$	$\omega_{6}$	$\omega_{7}$
Probability	$-0.1$	$0.2$	$0.3$	$0.4$	$-0.2$	$0.1$	$0.3$

$5$ persons entered a lift cabin on the ground floor of a $7$-floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first. The probability of all the $5$ persons leaving the cabin at different floors is

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The probability distribution of a discrete random variable $X$ is given below:
$X = x$ $-1$ $0$ $1$ $2$
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Then the value of $6 \Sigma(x^2) P(X=x) - \operatorname{var}(X) =$ ?

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$X$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$
$P(X)$ $0$ $k$ $2k$ $2k$ $3k$ $k^2$ $2k^2$ $7k^2 + k$