a) Please define mutually exclusive event?

b) Determine if the following events are mutually exclusive

i) Roll a dice: Get an even number, and get a number less than 3

ii) Roll a dice: Get a prime number (2,3,5), and get an odd number

iii) Select a student in the class. The student has blond hair, and the student has blue eyes

iv) Roll a dice. Get a number greater than 3, and get a number less than 3

c) In a deck of 52 cards, we have the following events:

A = event that the card selected is a Diamond

B = event that the card selected is a face card

C = event that the card selected is an ace

D = event that the card selected is a 5

E = event that the card selected is an 8 or a King

Which of the following events are mutually exclusive? State and explain your answers for each option below.

a. (A & B)

b. (A & C)

c. (B & C)

d. (B, C & D)

e. (B, C, D & E)

d) According to the Population census, 51.6% of the US adults are females, 10.4% of the US adults are divorced, and 6.0% of the US adults are divorced females.

For a US adult selected at random, let F = event the person is a female, and D = event the person is divorced

i) Obtain P(F), P(D), and P(F &D)

ii) Determine P(F or D)