BASIC CONCEPTS OF
PROBABILITY
EXAMPLES
EXPERIMENT
TOSSING A COIN
SAMPLE SPACE (S)
tail (T)
head (H)
S = {H, T}
EVENTS (E)
The event that a
head will occur.
E = {H}
The event that
even number
appears.
E = {2, 4, 6}
ROLLING A DIE
S = {1,2,3,4,5,6}
EXAMPLES
EXPERIMENT
SAMPLE SPACE (S)
EVENTS (E)
The event that an
even number will
come out.
E = {2h, 4h, 6h, 2T,
4T, 6T}
ROLLING A DIE &
TOSSING A COIN
S = {1H, 2H, 3H, 4H, 5H,6H,
1T, 2T, 3T, 4T, 5T, 6T}
The event that a tail
and odd number
will come out.
E = {1T, 3T, 5T}
EXAMPLES
EXPERIMENT
Identical number
cards (1, 2, … 10)
are placed in a
box and a card is
drawn at random
SAMPLE SPACE (S)
EVENTS (E)
S = {1, 2, 3, 4, 5, 6,
7, 8, 9, 10}
The event that the
number drawn is
prime.
E = {2, 3, 5, 7}
PROBABILITY OF SIMPLE EVENTS
EXAMPLES
1. A coin is tossed, find the probability of getting a head.
Sample Space (S) = {H, T}
n(head)
1
P(head) =
n(S) = 2
=
n(sample space)
2
Event = {H}
2. What is the probability of rolling a prime number on a number cube?
Sample Space (S) = {1, 2, 3, 4, 5, 6}
Event = {2, 3, 5}
n(3) = 3
n(S) = 6
n(E)
P(head) =
n(S)
EXAMPLES
A standard deck of cards has four suites: hearts, clubs, spades &
diamonds. Each suite has thirteen cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack,
queen and king. Thus the entire deck has 52 cards total.
EXAMPLES
3. A playing card is drawn at random from a standard deck of 52 playing
cards. Find the probability of drawing;
a. a diamond
P(a diamond) =
b. a black card
P(a black card) =
c. a queen
P(a queen) =
EXAMPLES
3. A playing card is drawn at random from a standard deck of 52 playing
cards. Find the probability of drawing;
n(E)
13
1
a. a diamond
P(a diamond) =
=
=
n(S)
52
4
b. a black card
n(E)
26
1
P(a black card) =
=
=
n(S)
52
2
c. a queen
n(E)
4
1
P(a queen) =
=
=
n(S)
52
13
EXAMPLES
4. Three coins are tossed. What is the probability of getting:
__________ a. three heads?
__________ b. two heads?
__________ c. one head?
__________ d. at least two tails?
__________ e. at most two tails?
__________ f. no tail?
EXAMPLES
4. Three coins are tossed. What is the probability of getting:
1
8
__________ a. three heads?
3
8
__________ b. two heads?
S = {HHH, HHT, HTH, HTT,
TTT, THH,THT, TTH}
n(S) = 8
3
8
__________ c. one head?
4 = 1
8
2
__________ d. at least two tails?
7
8
greater than or equal
__________ e. at most two tails? less than or equal
1
8
__________ f. no tail?
EXAMPLES
5. A bag contains 7 white balls and 11 orange balls.
a. If a ball is drawn at random from the bag, find the probability that
the ball is:
0
__________
i. green
7
18
__________
ii. white
11
18
__________
iii. not white
b. If 12 red balls are added to the bag and a ball is drawn from the bag.
Find the probability that ball is:
12 = 2
__________
i. red
30 5
18 = 3
__________
ii. not red
30 5
11
30
__________
iii. orange
EXAMPLES
6. Find the probability of the complement of each event.
a. Rolling a die and getting a 4.
1
5
1
=
1P(4) =
6
6
6
b. Selecting a letter of the alphabet and getting a vowel.
5
21
5
=
1P(vowel) =
26
26
26
c. Selecting a month and getting a month that begins with a J.
3
1
P(month that begins with a J) =
=
12
4