2­7 Probability of Compound Events 2010 web.notebook
December 07, 2010
2­7 Probability of
Compound Events
Check Skills You'll Need
Find each probability for one roll of a die.
OBJECTIVE
Find the probability of
independent and
dependent events.
1. P(multiple of 3)
2. P(greater than 4)
3. P(greater than 5)
4. P(greater than 6)
5. P(2 or 5)
6. P(less than 2 or 4)
Mar 25­2:00 PM
Feb 1­1:29 PM
Probability of Independent Events
COMPOUND EVENTS
P (A and B) = P (A) P (B)
Independent
Events
Dependent
Events
One event does NOT affect another event.
One event affects
another event.
When two events are
independent, you can
multiply to find the
probability that both occur.
Mar 25­2:20 PM
Mar 25­2:30 PM
Example: Suppose you toss a coin and roll a die. Find the probability of getting a heads on the coin and rolling a 5 on the die, or P (H and 5).
P (H) = 1
2
P (5) = 1
6
You Try!
Suppose you roll a red die and a blue die. What is the probability that you will roll a 3 on the red cube and an even number on the blue cube?
P(red 3) = 1/6
P (H and 5) = P (H) x P (5)
= 1 x
2
= 1
12
1
6
Mar 25­2:35 PM
P(blue even) = 3/6 = 1/2
P(red 3 and blue even) = Feb 1­1:34 PM
1
2­7 Probability of Compound Events 2010 web.notebook
Probability of Dependent Events
P (A and B) = P (A) P (B after A)
Remember: to use this formula, one event has to affect the other event.
Example: There are 3 discs in a CD player. The player has a "random" button that selects songs at random and does not repeat until all songs are played. What is the probability that the first song is selected from disc 3 and the second song is selected from disc 1? P (disc 3 song) = You Try!
Disc 1
(13 songs)
Disc 2
(7 songs)
10
30
Disc 3
(10 songs)
P (disc 1 song after disc 3 song) = 13
29
P (disc 3 song and disc 1 song) = Mar 25­2:44 PM
In a word game, you choose a tile at random from a bag containing the letter tiles shown. You DO NOT replace the first tile before you choose again. What is the probability that you will choose and A and then an E?
December 07, 2010
10
30
13
29
=
130
870
Mar 25­5:25 PM
?
IO
T
S
E
U
Q
?
S
N
?
How would the probability have changed if we DID replace the first tile before choosing the second tile?
Feb 1­1:43 PM
Mar 25­5:35 PM
HOMEWORK
Worksheet - front
and back - odds only
Mar 25­5:38 PM
2