Question

An experiment consists of tossing a die and then flipping a coin once if the number on the die is even. If the number on the die is odd, the coin is flipped twice. Use the notation "4H", for example, to denote the outcome that the die comes up "4" and the coin comes up "heads", and "3HT to denote the outcome that the die comes up 3 followed by a head and then a tail on the coin.

a. Construct a tree diagram to show the 18 elements of the Sample Space S.
b. List the elements corresponding to the event A that a number less than 3 occurs on the die.
c. List the elements corresponding to the event B that two tails occur.
d. List the elements corresponding to the event C that a head and tail occur.
e. List the elements corresponding to the event A'.
f. List the elements corresponding to the event A' ∩B.
g. List the elements corresponding to the event A ∪ B.
h. Draw a Venn diagram to illustrate events A, B, and C.
i. Are A and B mutually exclusive? Are A and C mutually exclusive? Are B and C mutually exclusive?

Answer 1

Kindly check attached picture and explanation

Explanation:

A.) The tree diagram is attached in the picture below.

B.) Number less than 3 :

Event A:

A = {1HH, 1HT, 1TT, 1TH, 2H, 2T}

C.)

Event B:

B = {1TT, 3TT, 5TT}

D.)

Event C:

C = {1HT, 1TH, 3HT,3TH,5HT, 5TH}

E.)

A' = Elements not in A = number ≥ 3

A' = {3HH,3HT, 3TT, 3TH, 4H, 4T, 5HH, 5HT, 5TH, 5TT, 6H, 6T}

Question f and G are not well formatted ;

h. Check attached picture

I) i. Are A and B mutually exclusive? Are A and C mutually exclusive? Are B and C mutually exclusive?

A and B are mutually exclusive if AnB = ∅

Check :

AnB = {1TT}

Hence, A and B are not mutually exclusive

A and C

AnC = {1HT, 1TH}

A and C are not mutually exclusive.

B and C

BnC = ∅

B and C are mutually exclusive