If you roll a pair of dice, what is the probability of rolling either a single 5 or a sum that is an even number?

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If you roll a pair of dice, what is the probability of rolling either a single 5 or a sum that is an even number?

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Answer 1 · 2015-10-28T08:20:47

$2/3$

Explanation:

Note that total number of possible cases are $6^2= 36$

Getting a single $5$ ( Say event $A$ ) means situation like as $(1,5),(2,5),(3,5),(4,5),(6,5),(5,1),(5,2),(5,3),(5,4),(5,6)$ i.e. $10$ cases and we have $18$ cases when sum is an even number ( Say event $B$ ) . But these two events are not mutually exclusive. Here $(1,5),(3,5),(5,1),(5,3)$ i.e. $4$ cases where we get a single $5$ as well as sum is a even number ( Say event $A nn B$ ) .

So we have number of favorable cases to our event $= n(A)+n(B)-n(A nn B) = 10+18-4=24$

So required probability $= 24/36=2/3$

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If you roll a pair of dice, what is the probability of rolling either a single 5 or a sum that is an even number?

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