Let two fair dice A and B be thrown. What is | vedclass

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(A) The total number of outcomes when two dice are thrown is $6 	imes 6 = 36$.Let $A$ be the outcome of the first die and $B$ be the outcome of the s

Vedclass · Accepted Answer

$\frac{5}{12}$

Vedclass · Answer

(A) The total number of outcomes when two dice are thrown is $6 	imes 6 = 36$.Let $A$ be the outcome of the first die and $B$ be the outcome of the second die. We want to find the number of outcomes where $A > B$.If $A=2$,$B=1$ ($1$ outcome).If $A=3$,$B=1, 2$ ($2$ outcomes).If $A=4$,$B=1, 2, 3$ ($3$ outcomes).If $A=5$,$B=1, 2, 3, 4$ ($4$ outcomes).If $A=6$,$B=1, 2, 3, 4, 5$ ($5$ outcomes).Total favorable outcomes $= 1 + 2 + 3 + 4 + 5 = 15$.The probability is $\frac{	ext{favorable outcomes}}{	ext{total outcomes}} = \frac{15}{36} = \frac{5}{12}$.

Let two fair dice $A$ and $B$ be thrown. What is the probability that the number appearing on dice $A$ is greater than the number appearing on dice $B$?

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