Question

Jake rolls two standard number cubes. Find the probability that the sum of the roll is 5, given that one cube came up even and the other came up odd.

Answer 1

Answer: Our required probability is
`(1)/(9)`

Explanation:

Since we have given that

One cube came up even.

Other cube came up odd.

We need to find the probability that the sum of the roll is 5.

so, Possible outcomes will be {(2,3), (4,1), (3,2), (1,4)}.

So, Number of possible outcomes = 4

Number of total outcomes = 36

So, probability that the sum is 5 is given by

`\frac{\text{Number of possible outcomes}}{\text{Total number of outcomes }}\\\\\\=(4)/(36)\\\\\\=(1)/(9)`

Hence, our required probability is
`(1)/(9)`

Answer 2

A sum of 5 from two cubes is ALWAYS one odd and one even, so the condition does not change anything whatsoever.
To roll a 5, we can have (1,4),(2,3),(3,2),(4,1) out of a sample space of 36 outcomes. So the probability is 4/36, or 1/9.