Page 212 - Math Course 3 (Book 2)

Probability of Compound Events

Dependent Events
At the school carnival, winners in the ring-toss
game are randomly given a prize from a bag that A gumball machine contains 16 red gumballs,
contains 4 sunglasses, 6 hairbrushes, and 5 key 10 blue gumballs, and 18 green gumballs. Once
chains. Three prizes are randomly drawn from the a gumball is removed from the machine, it is not
bag and not replaced. replaced. Find each probability if the gumballs are
removed in the order indicated.
Find P(hairbrush, hairbrush, key chain).
P(red, green, blue)
The selection of the first prize affects the
selection of the next prize since there is one A. 45
less prize from which to choose. So, the events 1331
are dependent.
B. 120
First Prize: 3311
6 ←number of hairbrush
195
P(hairbrush) = 15 ←total number of prizes C. 3311

Second Prize: D. 153
5 ←number of hairbrush 5324
P(hairbrush) =
14 ←total number of prizes
Answer
Third Prize:
5 ←number of key chains P(green, blue, not red)
P(key chain) = ←total number of prizes
13
A. 45
1331
P(hairbrush, hairbrush, key chain) =
P(hairbrush) • P(hairbrush) • P( key chain) B. 120
3311
6 5 5
= • • Substitution 195
15 14 13 C.
150 5 3311
= or Multiply
2730 91 Substitution
D. 153
5324
The probability of drawing
Answer hairbrush a hairbrush, and a key Answer
5
chain is .
91

Your Turn!

Independent Events

Two cities, Fairfield and Madison, lie on different faults. There is a 60% chance that Fairfield will experience
an earthquake by the year 2010 and a 40% chance that Madison will experience an earthquake by 2010.
Find the probability that both cities will experience an earthquake by 2010.

A. 60%
B. 40%
C. 24%
D. 100%

Answer

204