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)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.3: Binomial Probability
Problem 26E
Related questions
Question
A spinner has
equally sized sections,
of which are blue and
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?
10
8
2
Do not round your answer. (If necessary, consult a list of formulas.)
EXPLANATION
Events of this type are independent events.
To find the probability that two independent events
A
B
PA
=B · PAPB
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
10
P
|
landing on green |
|
=
|
number of ways the event can occurnumber of possible outcomes
|
=
|
210
|
|||
=
|
0.2
|
These
2
P
|
getting heads |
|
=
|
12
|
=
|
0.5
|
P
|
landing on green |
and | getting heads |
|
= P
|
landing on green |
·P
|
getting heads |
|
= 0.20.5
|
|||||||||
= 0.1
|
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