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?

Kindly check attached picture and explanation

Step-by-step 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

the degrees would remain the same ( the number to the left of the decimal point.

the multiply the decimal by 60 to get the minutes and use the numbers to the left of the decimal point.

then multiply the decimal portion of that by 60 for the seconds and round off as needed.

39 .956652

the 39 remains the degrees.

the minutes = 0.956652 x 60 = 57.39912

the minutes = 57

the seconds = 0.39912 x 60 = 23.95 = 24 ( rounded to nearest tenth)

so 39.956652 = 39 degrees, 57 minutes and 24 seconds

-75.159809

the -75 remains the degrees

the minutes = 0.159809 x 60 = 9.58854

the minutes = 9

the seconds = 0.58854 x 60 = 35.31, rounded to nearest tenth = 35.3 seconds

so -75.159809 = -75 degrees, 9 minutes and 35.3 seconds.

the first coordinate is north or south, since it it positive it is north.

the second number is east or west, because it is negative it is west.

39 degrees, 57 minutes and 24 seconds n

-75 degrees, 9 minutes and 35.3 seconds w

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