##### Question

In: Statistics and Probability

# A single die is rolled. Determine the probability of (show work) a) rolling a 6 given...

A single die is rolled. Determine the probability of (show work)

a) rolling a 6 given the number is even

b) rolling an even given the number is a 6

c) rolling a 5 given that the number is odd

d) rolling a 2 or a 6 given that the number is even

e) rolling a 4 given that the number is odd

## Solutions

##### Expert Solution

A single die is rolled.

Sample space = S = {1,2,3,4,5,6}

n(S) = 6

Let A be the event that number is even

A = {2,4,6}

n(A) = 3

Let B be the event that number is odd

B = {1,3,5}

n(B) = 3

a) rolling a 6 given the number is even

Let C be the event of rolling a 6

C ={6}

n(C) = 1

Required probability = P(C/A)

b) rolling an even given the number is a 6

Required probability = P(A/C)

c) rolling a 5 given that the number is odd

Let D be the event of rolling a 5

D = {5}

n(D) = 1

Required probability

= P(D/B)

d) rolling a 2 or a 6 given that the number is even

Let E be the event of rolling 2 or a 6

E = {2,6}

n(E) = 2

Required probability

= P(E/A)

e) rolling a 4 given that the number is odd

Let F be the event of rolling a 4

F = {4}

n(F) = 1

Required probability

= P(F/B)

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