A red and green die are rolled Find the probability of a the

A red and green die are rolled. Find the probability of

a. the red die gives 5

b. the sum is 6

c. the red die gives 5, given that the sum is 6

d. the sum is 6, given that the red die is 5

Are the events in parts a and b independent?

Solution

a)

P(red is 5) = 1/6 [ANSWER]

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b)

There are 6*6 = 36 outcomes possible, in which 5 will result to a sum of 6.

Hence,

P(6 sum) = 5/36 [ANSWER]

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c)

There are 5 possible ways to get a sum of 6, of which 1 result has a red 5.

So,

P(red is 5|sum is 6) = 1/5 [ANSWER]

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d)

There are 6 possible sums when the red die is fixed at 5. There is just 1 result to get a sum of 6 when teh red die is fixed at 5.

hence,

P(sum is 6|red is 5) = 1/6 [ANSWER]

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e)

NO, THEY ARE NOT INDEPENDENT.

As we can see, P(red is 5) =/= P(red is 5|sum is 6).