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What is the probability that at least one of a pair of fair dice lands of...

What is the probability that at least one of a pair of fair dice lands of 5, given that the sum of the dice is 8?

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Answer #1

Total outcomes of a pair of dice roll = 36

Outcomes when sum is 8 => (2,6) (3,5) (4,4) (5,3) (6,2)

#Outcomes when sum is 8 => 5

Probability ( Sum is 8 ) = 5/36

we need to find

Probability ( One dice lands 5 | Sum is 8) = Probability ( One dice lands 5 and Sum is 8) / Probability ( Sum is 8 )

outcomes

One dice lands 5 and Sum is 8 =>(3,5) (5,3)

# Outcomes One dice lands 5 and Sum is 8 = 2

Probability ( One dice lands 5 and Sum is 8) = 2/36

Probability ( One dice lands 5 | Sum is 8) = (2/36) / (5/36) = 2/5 = 0.40 or 40%

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