(A) The sample space of the experiment is $S = \{1, 2, 3, 4, 5, 6\}$.We determine the number of factors $(X)$ for each outcome:$X(1) = 1$ (factor: $1$

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$X = x$$1$$2$$3$$4$$P(X = x)$$1/6$$1/2$$1/6$$1/6$

(A) The sample space of the experiment is $S = \{1, 2, 3, 4, 5, 6\}$.We determine the number of factors $(X)$ for each outcome:$X(1) = 1$ (factor: $1$)$X(2) = 2$ (factors: $1, 2$)$X(3) = 2$ (factors: $1, 3$)$X(4) = 3$ (factors: $1, 2, 4$)$X(5) = 2$ (factors: $1, 5$)$X(6) = 4$ (factors: $1, 2, 3, 6$)Now,we calculate the probabilities for each value of $X$:$P(X = 1) = P(\{1\}) = 1/6$$P(X = 2) = P(\{2, 3, 5\}) = 3/6 = 1/2$$P(X = 3) = P(\{4\}) = 1/6$$P(X = 4) = P(\{6\}) = 1/6$Thus,the probability distribution is as shown in option $A$.

Class 12 Mathematics Probability Probability distribution

Easy

$A$ fair die with numbers $1$ to $6$ on its faces is thrown. Let $X$ denote the number of factors of the number on the uppermost face. Then the probability distribution of $X$ is

MHT CET 2023 All MHT CET

A
$X = x$ $1$ $2$ $3$ $4$
$P(X = x)$ $1/6$ $1/2$ $1/6$ $1/6$
B
$X = x$ $1$ $2$ $3$ $4$
$P(X = x)$ $1/6$ $1/6$ $1/6$ $1/2$
C
$X = x$ $1$ $2$ $3$ $4$
$P(X = x)$ $1/2$ $1/6$ $1/6$ $1/6$
D
$X = x$ $1$ $2$ $3$ $4$
$P(X = x)$ $1/6$ $1/6$ $1/2$ $1/6$

$X = x$	$1$	$2$	$3$	$4$
$P(X = x)$	$1/6$	$1/2$	$1/6$	$1/6$

$X = x$	$1$	$2$	$3$	$4$
$P(X = x)$	$1/6$	$1/6$	$1/6$	$1/2$

$X = x$	$1$	$2$	$3$	$4$
$P(X = x)$	$1/2$	$1/6$	$1/6$	$1/6$

$X = x$	$1$	$2$	$3$	$4$
$P(X = x)$	$1/6$	$1/6$	$1/2$	$1/6$

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The probability that an individual suffers a bad reaction from an injection is $0.001$. The probability that out of $2000$ individuals exactly three will suffer a bad reaction is:

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$A$ random variable $X$ has the following probability distribution:

$X$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$

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Determine $P(X > 6)$.

Easy

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Three balls are drawn at random from a bag containing $5$ blue and $4$ yellow balls. Let the random variables $X$ and $Y$ respectively denote the number of blue and yellow balls. If $\bar{X}$ and $\bar{Y}$ are the means of $X$ and $Y$ respectively,then $7 \bar{X} + 4 \bar{Y}$ is equal to ..........

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$A$ random variable $X$ takes the values $0, 1$ and $2$. If $P(X=1)=P(X=2)$ and $P(X=0)=0.4$,then the mean of the random variable $X$ is

MediumTS EAMCET 2002

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From a lot of $20$ baskets,which includes $6$ defective baskets,a sample of $2$ baskets is drawn at random one by one without replacement. The expected value of the number of defective baskets is

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

$A$ fair die with numbers $1$ to $6$ on its faces is thrown. Let $X$ denote the number of factors of the number on the uppermost face. Then the probability distribution of $X$ is

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The probability that an individual suffers a bad reaction from an injection is $0.001$. The probability that out of $2000$ individuals exactly three will suffer a bad reaction is:

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$A$ random variable $X$ has the following probability distribution:

$X$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$

$P(X)$ $0$ $k$ $2k$ $3k$ $3k^2$ $k^2$ $2k^2$ $7k^2+k$

Determine $P(X > 6)$.