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A spinner has  10  equally sized sections,  8  of which are blue and  2  of which are green. The spinner is spun and, at the same time, a fair coin is tossed. What is the probability that the spinner lands on green and the coin toss is heads? Do not round your answer. (If necessary, consult a list of formulas.)   EXPLANATION The event "landing on green" does not affect the event "getting heads."   Events of this type are independent events.   To find the probability that two independent events  A  and  B  both occur, we multiply the probabilities of the events. PA  and  =B · PAPB We want the probability of "landing on green" and "getting heads."   P landingon green   and   gettingheads   =  P landingon green ·P gettingheads     We must compute the two probabilities on the right-hand side.   Since the spinner has equally sized sections, each section is equally likely to be landed on.We have that  2  of the  10  sections are green, so we get the following. P landingon green   =   number of ways the event can occurnumber of possible outcomes     =   210     =   0.2 When a fair coin is tossed, the result is either heads or tails.These  2  results are equally likely, so we get the following. P gettingheads   =   12     =   0.5 We now multiply these probabilities to get the answer. P landingon green   and   gettingheads   =  P landingon green ·P gettingheads               =  0.20.5             =  0.1

A spinner has  10  equally sized sections,  8  of which are blue and  2  of which are green. The spinner is spun and, at the same time, a fair coin is tossed. What is the probability that the spinner lands on green and the coin toss is heads? Do not round your answer. (If necessary, consult a list of formulas.)   EXPLANATION The event "landing on green" does not affect the event "getting heads."   Events of this type are independent events.   To find the probability that two independent events  A  and  B  both occur, we multiply the probabilities of the events. PA  and  =B · PAPB We want the probability of "landing on green" and "getting heads."   P landingon green   and   gettingheads   =  P landingon green ·P gettingheads     We must compute the two probabilities on the right-hand side.   Since the spinner has equally sized sections, each section is equally likely to be landed on.We have that  2  of the  10  sections are green, so we get the following. P landingon green   =   number of ways the event can occurnumber of possible outcomes     =   210     =   0.2 When a fair coin is tossed, the result is either heads or tails.These  2  results are equally likely, so we get the following. P gettingheads   =   12     =   0.5 We now multiply these probabilities to get the answer. P landingon green   and   gettingheads   =  P landingon green ·P gettingheads               =  0.20.5             =  0.1

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.CR: Chapter Review
Problem 5CC: a What is meant by an experiment? Sample space? b What is an event? c Define the probability of an...
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Question
A spinner has 
10
 equally sized sections, 
8
 of which are blue and 
2
 of which are green. The spinner is spun and, at the same time, a fair coin is tossed. What is the probability that the spinner lands on green and the coin toss is heads?

Do not round your answer. (If necessary, consult a list of formulas.)

 
EXPLANATION
The event "landing on green" does not affect the event "getting heads."

 

Events of this type are independent events.

 

To find the probability that two independent events 
A
 and 
B
 both occur, we multiply the probabilities of the events.
PA
 and 
=B · PAPB
We want the probability of "landing on green" and "getting heads."

 

P
 landing
on green		   and   getting
heads
 
=  P
 landing
on green
·P
 getting
heads
 
  

We must compute the two probabilities on the right-hand side.

 

Since the spinner has equally sized sections, each section is equally likely to be landed on.
We have that 
2
 of the 
10
 sections are green, so we get the following.
P
 landing
on green
 
=  
number of ways the event can occurnumber of possible outcomes
 
 
=  
210
 
 
=  
0.2
When a fair coin is tossed, the result is either heads or tails.
These 
2
 results are equally likely, so we get the following.
P
 getting
heads
 
=  
12
 
 
=  
0.5
We now multiply these probabilities to get the answer.
P
 landing
on green		   and   getting
heads
 
=  P
 landing
on green
·P
 getting
heads
 
 
         
=  0.20.5
 
         
=  0.1
 
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