UI STAT 251 Fall 2010 Quiz 7 NAME:
UI #:
Class: 9:30
1. You bought a new set of four tires from a manufacturer who just announced a recall because 3% of those tires
are defective. What is the probability that none of your tire is defective?
P(none of your 4 tires is defective)=(1-P(tire is defective))^4=0.97^4=0.8853
2. A slot machine has three wheels that spin independently. Each has 10 equally likely symbols: 4 bars, 3 lemons, 2
cherries, and a bell. If you play, what is the probability that
a. you get 3 bells?
P(get 3 bell)=P(1st is a bell and 2nd is a bell and 3rd is a bell)=P(1st is a bell)*P(2nd is a bell)*P(3rd is a bell)
=(1/10)^3=0.001
b. you get no fruit symbols?
P(no fruit symbols)=(1st is not fruit and 2nd is not fruit and 3rd is not fruit)=(5/10)^3=0.125
c. you get no bars?
P(no bars)=(1st is not bar and 2nd is not bar and 3rd is not bar)=(6/10)^3=0.216
d. you get at least one bell?
P(you get at least one bell)=1-P(you get no nell)=1-(9/10)^3=0.271
3. In the real-estate ads suggest that 64% of homes for sale have garages, 21% have a swimming pools, and 17%
have both features.
a. If a home for sale has a garage, what is the probability that it has a pool too?
𝑃(𝑖𝑡 ℎ𝑎𝑠 𝑎 𝑝𝑜𝑜𝑙 𝑎𝑛𝑑 𝑎 𝑔𝑎𝑟𝑎𝑔𝑒)
𝑃(𝑖𝑡 ℎ𝑎𝑠 𝑎 𝑔𝑎𝑟𝑎𝑔𝑒)
P(it has a pool ǀ a home has a garage)=
0.17
= 0.64 = 0.2656
b. Are having a garage and a pool independent events? Compute and explain.
P(it has a pool)=0.21≠0.2656= P(it has a pool ǀ a home has a garage), so they are not independent. Because if
they are independent, these two values should be same.
c. Are having a garage and a pool mutually exclusive events? Compute and explain.
They are not mutually exclusive events. Because they have 17% overlap.
UI STAT 251 Fall 2010 Quiz 7 NAME:
UI #:
Class: 10:30
1. You bought a new set of four tires from a manufacturer who just announced a recall because 5% of those tires
are defective. What is the probability that none of your tire is defective?
P(none of your 4 tires is defective)=(1-P(tire is defective))^4=0.95^4=0.8145
2. A slot machine has three wheels that spin independently. Each has 10 equally likely symbols: 3bars, 4 lemons, 2
cherries, and a bell. If you play, what is the probability that
a. you get 3 bells?
P(get 3 bell)=P(1st is a bell and 2nd is a bell and 3rd is a bell)=P(1st is a bell)*P(2nd is a bell)*P(3rd is a bell)
=(1/10)^3=0.001
b. you het no fruit symbols?
P(no fruit symbols)=(1st is not fruit and 2nd is not fruit and 3rd is not fruit)=(4/10)^3=0.064
c. you get no bars?
P(no bars)=(1st is not bar and 2nd is not bar and 3rd is not bar)=(7/10)^3=0.343
d. you get at least one bell?
P(you get at least one bell)=1-P(you get no bell)=1-(9/10)^3=0.271
3. In the real-estate ads suggest that 68% of homes for sale have garages, 25% have a swimming pools, and 20%
have both features.
a. If a home for sale has a garage, what is the probability that it has a pool too?
𝑃(𝑖𝑡 ℎ𝑎𝑠 𝑎 𝑝𝑜𝑜𝑙 𝑎𝑛𝑑 𝑎 𝑔𝑎𝑟𝑎𝑔𝑒)
𝑃(𝑖𝑡 ℎ𝑎𝑠 𝑎 𝑔𝑎𝑟𝑎𝑔𝑒)
P(it has a pool ǀ a home has a garage)=
=
0.20
0.68
= 0.2941
b. Are having a garage and a pool independent events? Compute and explain.
P(it has a pool)=0.25≠0.2941= P(it has a pool ǀ a home has a garage), so they are not independent. If they are
independent, these two values should be same
c. Are having a garage and a pool mutually exclusive events? Compute and explain.
They are not mutually exclusive events. Because they have 20% overlap.