WHAT IS
PROBABILITY?
CLIL project
Class II C
ACTIVITIES
CLIL project
Class II C
KEY WORDS
1. The Puzzle
Find the words and eliminate the corresponding letters from the puzzle. The remaining letters form the name
of the French mathematician who first proposed the classical definition of probability.
CAR
CARD
CASE
COIN
DIE
DRAWING
EVENTS
GAMBLING
D
I
R
U
C
C
O
P
E
T
E
O
R
N
S
S
A
P
R
S
E
E
L
U
A
D
S
E
L
O
A
S
C
JACK
KING
LIKELY
OCCUR
O
M
T
W
R
O
T
B
C
T
A
O
J
N
C
I
A
T
A
A
G
P
H
A
I
G
O
N
C
B
S
A
S
OUTCOME
PASCAL
PICK
PROBABILITY
C
C
O
D
N
M
G
I
T
M
E
S
K
C
E
L
I
E
L
N
B
L
L
A
C
S
A
P
K
I
E
L
P
K
C
I
P
E
I
D
T
V
I
M
PROBABLE
ROLLING
SAMPLE SPACE
SCHOOL
G
N
I
L
L
O
R
Y
E
N
A
S
O
Y
L
E
K
I
L
C
G
S
SET
TEST
TOSS
R
A
C
P
R
O
B
A
B
L
E
2. Connect an English word with its Italian translation
CARD
COIN
DIE
to DRAW
EVENT
GAMBLING
JACK
KING
LIKELY
to OCCUR
OUTCOME
to PICK
PROBABILITY
to ROLL
SAMPLE SPACE
SET
TEST
to TOSS
SCEGLIERE A CASO
GETTARE (i dadi)
GIOCO D’AZZARDO
RISULTATO
DADO
CAPITARE
EVENTO
SPAZIO CAMPIONARIO
PROVARE
CARTA DA GIOCO
GETTARE (la moneta)
PROBABILITÀ
INSIEME
RE
PRENDERE
MONETA
PROBABILE
FANTE
3. Put in the spaces the correct words from the list of key words.
likely
a) The word _____________,
____________,
probable and hazardous are synonyms.
coin
outcome
b) Tossing a ___________ I got head. Head is the _____________
of my experiment.
c) All the possible outcomes that can occur when I execute the experiment form the sample
______________.
space
d) The _________,
the Queen and the ____________
are three cards of a pack.
Jack
King
probability
e) The measure of how likely an event is, is called ________________.
set
event
f) The particular outcome or __________
of outcomes we are interested in, is an _________.
g) ____________
is dangerous for our pocket!
Gambing
Name and Surname ___________________
ACTIVITY 2: PROBABILITY
1. There are three possible ways to find probability:
LACISCASL EINFTIDON, QFIUSTTNEERU EFDOTNINI, ECJTIUVBSE IBLIARTBYOP.
CLASSICAL DEFINITION FREQUENTIST DEFINITION SUBJECTIVE PROBABILITY
__________ __________, ___________ ___________, _____________ ___________.
2. Write a phrase about Bruno De Finetti.
Bruno De Finetti proposed the subjective theory of Probability and he worked in Triest in
______________________________________________________________________
the first half of the XX century (University, Assicurazioni Generali)
______________________________________________________________________
3. Complete the formula for the classical definition of Probability:
favourable
Probability Of An Event P(A) = The Number of __________________cases
The number of
cases
possible
4. Theprobability
________________ of event A is the number of ways event A can occurdivided
___________ by the
total number of possibleoutcomes
___________. The probability of event A is the number offavourable
____________
cases
cases (outcomes) divided by the total number of possible ______________
(outcomes).
cases
divided
favourable
outcomes
probability
5. Exercises:
a) What is the probability of rolling an even number with a die? 3/6 = 1/2
b) In a bag we have 10 pens: 3 green, 4 red and the remaining blue. Picking a pen up, what is
the probability of picking a green one? What is the probability for a red one?3/10 4/10
c) Playing Tombola, what is the probability of drawing a multiple of 7? 12/90 =6/45
d) In a box we have 5 candles, three used and two new ones. What is the probability of drawing
a new one from the box?
2/5
6. Which of the following events are certain and which impossible? In the last column, write the
appropriate probability (zero or one).
What is the probability that…
EVENT
…rolling a die, a number greater than 8 is drawn?
… in a this year Formula 1 race, Alex Del Piero wins?
… playing tombola, a number less than 100 is drawn?
certain
X
X
… in the today Mathematics test, Lisa receives 12 (she’s is very good, indeed!)?
… Giovanni works in Nolandia (?)?
… rolling two dice, the sum of the numbers is 20?
… choosing a letter from the alphabet, it’s a consonant or a vowel.
… picking a card up from an ordinary pack, it’s a 15 of clubs.
… choosing a boy among your schoolmates, he is a Carducci student?
… this morning you don’t meet a Lunar girl?
impossible
X
X
X
X
X
X
X
X
P(A)
0
0
1
0
0
0
1
0
1
1
ACTIVITY 3
Crossword: the Theory of probability
1
2
3
J A C K
A
4
5
6
P
S
FO
R E Q U E N T I
T
ON E
S
S T
B
7
8
DR A W
L
A
9
F B V OR A B L E
I
P
F
10
L
L
L I K E L Y
11
H E A D
I
N
12
C
CE R T A I N
T
E
T
Y
T
13
C OI N
A
14
Z E R O
D
Across:
Down:
1
It's a card with the image of a soldier
2
In Italiano it's "caso"
4
The probability of a certain event
3
The verb for a coin
6
The probability definition which involves
frequency
5
The measure of how probable an event is
7
The "De", famous French mathematician
8
In Italian it's: scegliere a caso
In the Laplace's formula, these are the cases at
the numerator
8
9
Famous Italian mathematician who proposed the
subjective theory of probability
13
A jack is a .....
10
Synonym of probable
11
In the coin, it's the opposite of tail
12
An event which has P(A)=1
13
The object I toss
14
The probability of an impossible event
EXERCISES
1. In a sack we have three blue little balls, two white balls and four yellow balls. Which is the
probability of drawing a blue ball from the sack? Which is the probability of drawing any
ball except a blue one? (use complement definition)
P(blue)=3/9=1/3 P(not blue)= 1 – 1/3=2/3
2. In an ordinary pack (for “briscola”) there are 40 cards. Four of those are jacks. Drawing a
card, which is the probability of getting a jack? Which is the probability of drawing any
card, except a jack? (use complement definition)
P(jack)=4/40=1/10 P(not jack)= 1 – 1/10=9/10
3. Which is the probability of drawing from the sack a Tombola number bigger than 75?
Which is the probability of drawing a number less or equal to 75? (use complement
definition).
P(>75)=15/90=1/6 P(not >75)= 1 – 1/6=5/6
4. Rolling a die, which is the probability of rolling an odd number? And which is the
probability of rolling an even number? (use complement definition)
P(odd)=3/6=1/2 P(even: not odd)= 1 – 1/2=1/2
5. I’m thinking about a day of the year. Which is the probability that it is exactly your
birthday? Which is the probability that isn’t your birthday? (use complement definition).
P (your birthday)=1/365 P(not your birthday)= 1 – 1/365=364/365
6. Three pens are good and five are not. Drawing one pen of the set, which is the probability of
drawing a good pen? Which is the probability of getting a bad one? (use complement
definition).
P(good)=3/8 P(bad: not good)= 1 – 3/8=5/8
7. If I have a probability equal to 0,23 to complete this activity in half an hour, which is the
probability that I will not complete it in half an hour? (use complement definition).
P(I complete)=0,23 P(I don’t complete)= 1 – 0,23 = 0,77
8. A party has a probability P(A)=0,73 of winning the elections. Which is the probability that
this party loses? (use complement definition).
P(wins)=0,73 P(loses: doesn’t win)= 1 – 0,73 = 0,27
9. Which is the probability of rolling a 7 with an ordinary die? Which is the probability of
rolling any number except a 7? (use complement definition). P(7)=0 P(not 7)= 1 – 0 = 1
Name and Surname______________________________
ACTIVITY 4. COMPOUND EVENT
I) Answer to the following questions:
a) Which is the key conjunction in the compound event?
1) OR
2) AND
3) BECAUSE
4) THAT





b) When two events are independent?
1) When they are logically connected.
2) When the fact that A occurs affects the probability of B occurring.
3) When one follows the other.
4) When the fact that A occurs does not affect the probability of B occurring.




c) Which is the arithmetical operation for the calculation of a compound event?
1) Subtraction
2) Addition
3) Division
4) Multiplication




d) In Theory of probability the symbol P(B | A) means that
1) the probability of event B must be divided by the probability of event A
2) the probability of event B is influenced by the fact that event A has occurred
3) the probability of event B must be divided by the probability of event A
4) the probability of event B is not influenced by the fact that event A has occurred




e) If you draw a coloured ball from a sack (event A) and then you draw another one (event B),
the two events:
are always independent
are never independent
are independent only if we put back (replace) the first ball in the sack
are independent only if we don’t put back (replace) the first ball in the sack




II) In the table we have nine couples of events (event A; event B). Indicate the couples of
dependent (D) events and of independent events (I)
EVENT A
EVENT B
I
1
Rolling a die, number 3 is drawn
Rolling the same die, number 4 is drawn
x
2
Picking a card, it’s a king
Picking a card from the same pack without replacement, it’s a
jack
3
Picking a card, it’s a king
Picking a card from the same pack with replacement, it’s a
four
4
A man chosen randomly is a smoker
A man chosen randomly is affected by heart diseases
x
5
One of you, chosen randomly, likes
English
One of you, chosen randomly, likes CLIL course
x
6
Number 37 is drawn, playing Tombola.
Number 43 is drawn, playing Tombola
x
7
Schumacher wins the next F1
Championship
Juventus wins 2005-2006 Italian football championship
8
Schumacher wins
A Ferrari car wins
x
9
Number 18 is drawn at roulette
Number 12 is drawn at roulette
x
III)
x
LINE1:
P(B)
dependent/independent
EVENT A: rolling a die, number 3 is drawn;
1/6
1/6
x
P(compound event)
EVENT B Rolling the same die, number 4 is drawn
independent
P = 1/6  1/6 = 1/36
LINE2:
4/52
4/51
dependent
4/52
independent
P=4/52  4/51=16/2652
LINE3:
4/52
LINE9:
1/37
P=4/52  4/52=16/2704
[in roulette there are 37 numbers]
1/37
independent
P=1/37  1/37=1/1369
x
x
Calculate the probabilities of the compound events formed by the two events on a
line in the table (lines: 1,2,3,9) (look at the example of line 1)
P(A)
D
Name and Surname______________________________
ACTIVITY 5. MUTUALLY EXCLUSIVE EVENTS
Crossword
1
I ND I P E ND EN T
N
2
M U L T I P L I C AT I O N
Across:
1.
2.
3.
6.
E
OR
7.
3
4
8.
9.
5
M
D
S
6
E X CL U S S
I V E
C
J
T
O
U
T
U
A DD I T I O N
7
L
O
AN D
8
L
Y
I
Down:
1.
4.
5.
The operation between sets which involves the
compound event. Its symbol is .
Two events are _________ exclusive , if it is
impossible for them to occur together.
We say "mutually exclusive" events or _______
events
II) In the table we have nine couples of
events (event A; event B). Indicate the couples
of mutually exclusive (disjoint D) events and of
not mutually exclusive (NME)
9
V EN N
T
EVENT A
1
2
3
4
5
6
7
8
9
Two events, A and B, are _____ if the fact that A
occurs does not affect the probability of B occurring.
The "rule" for compound event.
The "key" conjunction for two independent events
when I ask that one of them occurs
Two events are mutually ____ if it is impossible for
them to occur together.
The "rule" for finding the probability in the "OR"
case.
The "key" conjunction for the compound event
____’s diagrams show the sets we are studying
Number 32 is drawn, playing Tombola
Rolling a die, a 3 is drawn
Drawing a cards it’s a club
Schumacher wins
Schumacher wins
Choosing randomly a letter, it’s a vowel
Rolling a die an odd number is drawn
Choosing randomly a day, it’s in March
Choosing randomly a song, it’s sung in English
EVENT B
Number 87 is drawn, playing Tombola
Rolling a die, a 4 is drawn
Drawing a card, it’s a king
Alonso wins
A Ferrari car wins
Choosing randomly a letter, it’s a consonant
Rolling a die a multiple of 3 is drawn
Choosing randomly a date, it’s an odd number
Choosing randomly a song, it’s sung by an American singer
ME
NME
x
X
X
X
X
X
X
X
X
III) Find the probability of the events formed by the following couples of disjoint events:
Event A: “Rolling a die, a 3 is drawn”
1/6
P(A) = _______
Event B: “Rolling a die, a 5 is drawn”
1/6
P(B) = _______
Which is the probability of rolling a 3 OR a 5 on a die? 1/6 + 1/6 =2/6
Event A: “Drawing a card it’s a spade”
1/4
P(A) = _______
Event B: “Drawing a card it’s a club”
1/4
P(B) = _______
Which is the probability of drawing a spade OR a club from an ordinary deck? 1/4 + 1/4 =1/2
Event A: “Getting number 31 at the roulette”
P(A) = 1/37
_______
Event B: “Getting number 37 at the roulette”
0/37
P(B) = _______
Which is the probability of getting a 31 OR a 37 at the roulette? 1/37 + 0/37 =1/37
7/90
Event A: “Drawing a Tombola number, it’s a multiple of 13”
P(A) = _______
Event B: “Drawing a Tombola number, it’s a multiple of 9”
P(B) =
_______
9/90
Which is the probability of drawing a multiple of 13 OR a multiple of 9? 7/90 + 9/90 =16/90
Event A: “the probability that tomorrow it’ll be cloudy is 0,45”
Event B: “the probability that tomorrow it’ll be snowy is 0,15”
Which is the probability that tomorrow it will be cloudy OR snowy? 0,45+0,15 =0,60
In a jar there are 14 coloured marbles: 6 green, 3 red, 5 blue ones.
Event A: “A green marble is drawn”
P(A) = _______
6/14
5/14
Event B: “A blue marble is drawn”
P(B) = _______
Which is the probability that a green OR a blue marble is drawn? 6/14 + 5/14 =11/14
Name and Surname__________
ACTIVITY 6. TOTAL PROBABILITY and REVIEW
I)
Find the probability of the events formed by the following couples of not disjoint events:
Event A: “Rolling a die, a multiple of 2 is drawn”
P(A) = 3/6
Event B: “Rolling a die, a multiple of 3 is drawn”
P(B) = 2/6
Event (AB): “Rolling a die, a multiple of 2 and a multiple of 3 is drawn” P (AB) = 1/6
Which is the probability of rolling a multiple of 2 OR a multiple of 3 on a die?
P (AB)=3/6 + 2/6 – 1/6 = 4/6
13/52
Event A: “Drawing a card it’s a heart”
P(A) = _______
Event B: “Drawing a card it’s a face”
P(B) = _______
12/52
3/52
Event (AB): “Drawing a card, it’s a heart and a face”
P (AB) = _______
Which is the probability of drawing a heart OR a face from an ordinary deck?
P (AB)= 13/52+12/52-3/52
7/90
Event A: “Drawing a Tombola number, it’s a multiple of 12”
P(A) = _______
9/90
Event B: “Drawing a Tombola number, it’s a multiple of 10”
P(B) = _______
Event (AB): “Drawing a number, it’s a multiple of 12 OR a multiple of 10”
1/90
P (AB) = _______
Which is the probability of drawing a multiple of 12 OR a multiple of 10?
P (AB)= 7/90+9/90-1/90=15/90
In a jar there are 25 coloured marbles: 6 green and big, 8 green and small, 5 blue and
big, 6 blue and small.
14/25
Event A: “A green marble is drawn”
P(A) = _______
11/25
Event B: “A big marble is drawn”
P(B) = _______
Event (AB): “Drawing a marble, it’s green and big”
P (AB) = _______
6/25
Which is the probability that a green OR a big marble is drawn?
P (AB)= 14/25+11/25-6/25=19/25
II)
Solve the following exercises (repetition):
1. What is the probability that choosing randomly among the students of your own class for a
test, the chosen student is exactly you?
2. What is the probability that in this year Formula 1 race, Alex Del Piero wins?
3. What is the probability that choosing a boy among your schoolmates, he is a Carducci
student?
4. In a sack we have three blue little balls, two white balls and four yellow balls. Which is the
probability of drawing a blue ball from the sack? Which is the probability of drawing any
ball except a blue one? (use complement definition)
5. I’m thinking about a day of the year. Which is the probability that it is exactly your birthday?
Which is the probability that isn’t your birthday? (use complement definition).
6. What is the probability that, picking a card, it’s a king and afterwards, picking another card
from the same deck with replacement, it’s a four?
7. Playing Tombola number 33 is drawn and, afterwards, number 12 is drawn. Which is the
probability of this compound event?
8. Which is the probability of rolling a 3 OR a 5 on a die?
9. If the probability that tomorrow it’ll be cloudy is 0,45 and the probability that tomorrow it’ll
be snowy is 0,15, which is the probability that tomorrow it will be cloudy or snowy?
10. Playing Tombola, which is the probability of drawing a multiple of 12 or a multiple of 10?