Download Lesson 3 Compound Events

INVESTIGATION
Write down the sample space for throwing a die and
tossing a coin.
1T
2T
3T
4T
5T
6T
1H
2H
3H
4H
5H
6H
From the sample space calculate:
1
P(Head) =
2
2 1
P(Multiple of 3 and a Head) =
=
12 6
P(Multiple of 3) = 4 = 1
12 3
1 1
1
´
=
P(Multiple of 3) x P(Head) =
3 2 6
NOTE 4: COMPOUND EVENTS
Independent Events
Two events A and B are independent if the
occurrence of one does not affect the occurrence
of the other.
If A and B are independent events then:
P(A and B) = P(A) x P(B)
Example: A coin is tossed and a tetrahedron die
(1-4) is rolled. What is the probability of a head
on the coin and a four on the die.
P(Head and a four) = P(Head) x P(Four)
=
=
x
1
2
1
8
1
4
Dependent Events
Two events A and B are dependent if the
occurrence of one does affect the occurrence of
the other.
If A and B are dependent events then:
P(A then B) = P(A) x P(B given that A has occurred)
Example: Two cards are drawn from a pack of 52,
one after the other.
The first card is not replaced before the second
card is drawn. What is the probability that both
cards are Aces?
P(2 cards drawn are Aces)
= P(First card is Ace) x P(Second is Ace given first is Ace)
=
4
52
=
1
221
x
3
51
Standard Level:
Page 482
Exercise 19E.1 – E.2
Studies:
Page 506
Exercise 16E.1 – E.2