Page 178 - Math Course 1 (Book 2)

Probability and Composite Events

Probability of Dependent Events
Key Concept

Example
Probability of Mutually
Exclusive Events

Words The probability of one or the other of CLOTHES
two mutually exclusive events can be Charlie’s clothes closet contains 3 blue shirts,
found by adding the probability of the 10 white shirts, and 7 striped shirts. What is the
f rst event to the probability of second probability that Charlie will reach in and randomly
event. select a white shirt followed by a striped shirt?

10 7
Symbols P(A or B) = P(A) + P(B) P(white shirt and striped shirt) = • 19
20
70
4 18 11 = • 7
Example P(5 or even) = + or 380 38
36 36 18
The probability of Charlie will
Answer
select a white shirt followed by
7
a striped shirt is 38
Let’s Begin

Probability of Mutually Exclusive Events
Probability of Independent Events
Example

Example You draw a card from a standard deck of playing

cards. What is the probability that the card will be
a black nine or any heart?
GAMES
In a popular number cube game, the highest pos- The events are mutually exclusive because the
sible score in a single turn is a roll of f ve of a kind. card cannot be both a black nine and a heart at the
After rolling one f ve of a kind, every other f ve of a same time.
kind you roll earns 100 points.
P(black nine or heart) = P(black nine) + P(heart)
What is the probability of rolling two f ve of a kinds
2
in a row? = + 13
52 52
15
The events are independent since each roll does =
not affect the outcome of the next roll. 52

There are six ways to roll f ve of a kind, (1, 1, 1 ,1, 1), The probability of wild card will
5
(2, 2, 2, 2, 2), and so on, and there are 6 or 7776 Answer be a black nine or any heart is
15
ways to roll f ve dice. So, the probability of rolling 52
f ve of a kind on a toss of the number of cubes is
1
6
or
7776 1296
P(two f ve of a kind) =
P(f ve of a kind on f rst roll) • P(f ve of a kind on second roll)
1 1
= •
1296 1296
= 1
1,679,616
The probability of rolling two f ve
Answer of a kind in a row is
1
1,679,616
170