Unizor - Probability - Definition - Problems 1

There are 8 people in the room:
A - male, 19 years of old;
B - male, 18 years of old;
C - female, 18 years of old;
D - male, 20 years of old;
E - male, 24 years of old;
F - female, 28 years of old;
G - male, 33 years of old;
H - female, 16 years of old.
Our random experiment consists of selecting one of them.

(a) What are the set and its elements representing the result of this random experiment and its elementary events? What is the measure of probability of an entire sample space?
Answer:
{A,B,C,D,E,F,G,H}; Pa=1

(b) What is the measure of probability allocated to each elementary event?
Answer:
Pb=1/8

(c) What is the subset that represents the event "Randomly selected person is a female"? What is its measure of probability?
Answer:
{C,F,H}; Pc=3/8

(d) What is the subset that represents the event "Randomly selected person is a male"? What is its measure of probability?
Answer:
{A,B,D,E,G}; Pd=5/8

(e) What is the subset that represents the event "Randomly selected person is older than 20 years"? What is its measure of probability?
Answer:
{E,F,G}; Pe=3/8

(f) What is the subset that represents the event "Randomly selected person is a female AND older than 20 year"? What is its measure of probability?
Answer:
{C,F,H}∩{E,F,G}={F}; Pf=1/8

(g) What is the subset that represents the event "Randomly selected person is a person"? What is its measure of probability?
Answer:
{A,B,C,D,E,F,G,H}; Pg=1

(h) What is the subset that represents the event "Randomly selected person is younger then 10 year old"? What is its measure of probability?
Answer:
{}=∅; Ph=0

(i) What is the subset that represents the event "Randomly selected person is NOT younger then 10 year old"? What is its measure of probability?
Answer:
{A,B,C,D,E,F,G,H}; Pi=1

(j) What is the subset that represents the event "Randomly selected person is NOT younger then 25 year old AND is NOT a male"? What is its measure of probability?
Answer:
{F,G}∩{C,F,H}={F}; Pj=1/8

(k) What is the subset that represents the event "Randomly selected person is NOT younger then 25 year old OR is a male"? What is its measure of probability?
Answer:
{F,G}∪{A,B,D,E,G}=
={A,B,D,E,F,G}; Pk=6/8=3/4

(l) What is the subset that represents the event "Randomly selected person is NOT a male OR NOT older than 20 years old"? What is its measure of probability?
Answer:
{C,F,H}∪{A,B,C,D,H}=
={A,B,C,D,F,H}; Pl=6/8=3/4

(m) What is the subset that represents the event "Randomly selected person is NOT a male AND NOT older than 20 years old"? What is its measure of probability?
Answer:
{C,F,H}∩{A,B,C,D,H}=
={C,H}; Pm=2/8=1/4