Two dice are thrown simultaneously. If X deno | vedclass

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Question

(A) Here,$X$ represents the number of sixes obtained when two dice are thrown simultaneously.Therefore,$X$ can take the values $0, 1,$ or $2$.$P(X=0)

Vedclass · Accepted Answer

$1/3$

Vedclass · Answer

(A) Here,$X$ represents the number of sixes obtained when two dice are thrown simultaneously.Therefore,$X$ can take the values $0, 1,$ or $2$.$P(X=0) = P(	ext{not getting six on any of the dice}) = \frac{5}{6} 	imes \frac{5}{6} = \frac{25}{36}$$P(X=1) = P(	ext{six on first die and no six on second die}) + P(	ext{no six on first die and six on second die}) = \left(\frac{1}{6} 	imes \frac{5}{6}ight) + \left(\frac{5}{6} 	imes \frac{1}{6}ight) = \frac{10}{36}$$P(X=2) = P(	ext{six on both the dice}) = \frac{1}{6} 	imes \frac{1}{6} = \frac{1}{36}$The probability distribution is:						$X$			$0$			$1$			$2$							$P(X)$			$\frac{25}{36}$			$\frac{10}{36}$			$\frac{1}{36}$			Expectation of $X = E(X) = \sum X_i P(X_i) = (0 	imes \frac{25}{36}) + (1 	imes \frac{10}{36}) + (2 	imes \frac{1}{36})$$E(X) = 0 + \frac{10}{36} + \frac{2}{36} = \frac{12}{36} = \frac{1}{3}$

Expenses	$0$	$500$	$1000$	$1500$	$2000$	$2500$	$3000$
Probability	$0.35$	$0.25$	$0.15$	$0.10$	$0.08$	$0.05$	$0.02$

$X$	$0$	$1$	$2$	$3$	$4$
$P(X)$	$0.1$	$0.5$	$0.2$	$-0.1$	$0.3$

Two dice are thrown simultaneously. If $X$ denotes the number of sixes,find the expectation of $X$.

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