(B) For any probability distribution defined on a sample space $S$,two conditions must be satisfied:$1$. For each outcome $\omega_{i} \in S$,the proba

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The assignment is invalid because probabilities are negative.

(B) For any probability distribution defined on a sample space $S$,two conditions must be satisfied:$1$. For each outcome $\omega_{i} \in S$,the probability $P(\omega_{i})$ must satisfy $0 \leq P(\omega_{i}) \leq 1$.$2$. The sum of all probabilities must be equal to $1$,i.e.,$\sum P(\omega_{i}) = 1$.In the given table,we observe the probabilities for $\omega_{1}$ and $\omega_{5}$ are $-0.1$ and $-0.2$ respectively.Since $P(\omega_{1}) = -0.1 Therefore,this assignment of probabilities is not valid.

Class 12 Mathematics Probability Probability distribution

Easy

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 $-0.1$ $0.2$ $0.3$ $0.4$ $-0.2$ $0.1$ $0.3$

A
The assignment is valid.
B
The assignment is invalid because probabilities are negative.
C
The assignment is invalid because the sum of probabilities is not $1$.
D
The assignment is invalid because the number of outcomes is $7$.

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Class 12

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Probability

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Probability distribution

$A$ bag contains $2$ white and $1$ red balls. One ball is drawn at random and then put back in the box after noting its colour. The process is repeated again. If $X$ denotes the number of red balls recorded in the two draws,describe $X$.

Easy

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$A$ card is drawn from a pack of $52$ playing cards. The card is replaced and the pack is shuffled. If this process is repeated $6$ times,what is the probability that $2$ hearts,$2$ diamonds,and $2$ black cards are drawn?

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Let $F(x)$ be the cumulative distribution function (c.d.f.) of a continuous random variable $X$. If $F(b) = 0.7$ and $P(X > a) = 0.4$, then the value of $P(a < X < b)$ is ...

DifficultMHT CET 2026

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$A$ random variable $X$ has the following probability distribution:
$X$ $0$ $1$ $2$
$P(X)$ $\frac{25}{36}$ $k$ $\frac{1}{36}$

If the mean of the random variable $X$ is $\frac{1}{3}$,then the variance is:

$X$	$0$	$1$	$2$
$P(X)$	$\frac{25}{36}$	$k$	$\frac{1}{36}$

MediumKCET 2024

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$A$ person draws a card from a pack of $52$ cards and replaces it. After shuffling,he draws a card again. If he repeats this process,what is the probability that he draws a red card for the first time on the third draw?

Medium

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

Similar Questions

$A$ bag contains $2$ white and $1$ red balls. One ball is drawn at random and then put back in the box after noting its colour. The process is repeated again. If $X$ denotes the number of red balls recorded in the two draws,describe $X$.

$A$ card is drawn from a pack of $52$ playing cards. The card is replaced and the pack is shuffled. If this process is repeated $6$ times,what is the probability that $2$ hearts,$2$ diamonds,and $2$ black cards are drawn?

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$A$ random variable $X$ has the following probability distribution:
$X$ $0$ $1$ $2$
$P(X)$ $\frac{25}{36}$ $k$ $\frac{1}{36}$

If the mean of the random variable $X$ is $\frac{1}{3}$,then the variance is: