A fair die with numbers 1 to 6 on its faces i | vedclass

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(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$

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(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 $A$.

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

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

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

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