Question

A fair, six-sided die is rolled. Describe the sample space S, identify each of the following events with a subset of S and compute its probability (an outcome is the number of dots that show up). a. Event T = the outcome is three.

b. Event A = the outcome is an odd number

c. Event B = the outcome is less than four.

d. Event D = the complement of A

e. A AND B

f. A OR B

g. Event N = the outcome is a prime number.

i. Event K = the outcome is seven.

Answer 1

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

a) T = {3}

P(T) = 1/6

b) A = {1, 3, 5}

P(A) = 3/6 = 1/2

c) B = {1, 2, 3}

P(B) = 3/6 = 1/2

d) D = S - A = {2, 4, 6}

P(D) = 3/6 = 1/2

e) A and B = {1, 3}

P(A and B) = 2/6 = 1/3

f) A or B = {1, 2, 3, 5}

P(A or B) = 4/6 = 2/3

g) N = {2, 3, 5}

P(N) = 3/6 = 1/2

i) K = { } [empty set because only 1 to 6 are possible]

P(K) = 0/6 = 0

Please comment if any doubt. Thank you.