##### Question

In: Statistics and Probability

# A three-sided fair die with faces numbered 1, 2 and 3 is rolled twice. List the...

A three-sided fair die with faces numbered 1, 2 and 3 is rolled twice. List the sample space. S =

b.{ List the following events and their probabilities. Write probabilities in non-reduced fractional form A = rolling doubles = { P(A)= / B = rolling a sum of 4 = { P(B)= / C = rolling a sum of 5 = { P(C)=

C. Are the events A and B mutually exclusive? If yes, why? If not, why not?

D.Are the events B and C mutually exclusive? If yes, why? If not, why not?

E. Find the following probabilities: P(A and B)= / P(B or C)= / P(B and C)=

## Solutions

##### Expert Solution

Question (a)

A three-sided fair die with faces numbered 1, 2 and 3 is rolled twice

Sample Space S = { (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3) }

Question (b)

Total number of outcomes possible = 9

A = rolling doubles

Outcomes where doubles will roll are (1,1), (2,2), (3,3)

So Number of outcomes for A = 3

So P(A) = 3/9

B = rolling a sum of 4

Outcomes where sum will be 4 on both rolls are (1,3), (2,2), (3,1)

So Number of outcomes for B = 3

So P(B) = 3/9

C = rolling a sum of 5

Outcomes where sum will be 5 on both rolls are (2,3), (3,2)

So Number of outcomes for C = 2

So P(C) = 2/9

Question (c)

Are the events A and B mutually exclusive?

Two events A and B are said to be mutually exclusive if they don't have any common outcomes between them

Here A and B have a common outcome which is (2,2)

So events A and B are not mutually exclusive

Question (d)

Are the events B and C mutually exclusive?

Two events B and C are said to be mutually exclusive if they don't have any common outcomes between them

Here B and C do not have any common outcome between them

So events B and C are mutually exclusive

Question (e)

P(A and B)

The number of common outcomes between A and B is 1 which is (2,2)

So P(A and B) = 1/9

P(B or C)

P(B or C) = P(B) + P(C) - P(B and C)

B and C does not have any common outcomes between them, So P(B and C) = 0

P(B or C) = P(B) + P(C)

= 3/9 + 2/9

= 5/9

P(B or C) = 5/9

B and C does not have any common outcomes between them, So P(B and C) = 0

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