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taniyahbenyamin2
06.03.2020 •
Mathematics
From the following list of hypothetical situations, identify those that are independent events using the given probabilities of each event and the formal definition of independence.
a. In a yearly weather survey of a city, 32% of the days had precipitation, 25% of the days were weekend days, and 8% of the days had precipitation and were weekend days
b. In a voter study, 25% of the voters had a low income, 45% of the voters were registered Democrats, and 15% of voters had a low income and were registered Democrats.
c. In a study of color blindness, 10% of the individuals were color-blind, 52% of the individuals were male, and 8% of the individuals were color-blind and were male.
d. In a college course survey, 20% of students received an A in chemistry, 25% of students received an A in biology, and 5% of students received an A in both chemistry and biology.
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Ответ:
Step-by-step explanation:
Hello!
Be two events A and B of the sample space S. A and B are independent when the ocurrence of A doesn't affect the probability of occurrence of B.
Symbolically:
P(B/A)= P(B) -or- P(A/B)= P(A)
If A and B are not independent then P(B/A) ≠ P(B) -or- P(A/B)≠ P(A)
P(A∩B)= P(A)*P(A/B)
a.
A: "the day had precipitation" ⇒ P(A)= 0.32
B: "the day was a weekday" ⇒ P(B)= 0.25
P(A∩B)= 0.08
To check if both events are independent you have to calculate the conditional probability between them and compare it with the probability of the event alone:
Then P(B/A)= P(B) ⇒ A and B are independent.
b.
A: "the voter had low income" ⇒ P(A)= 0.25
B: "the voter is a registered Democrat" ⇒ P(B)= 0.45
P(A∩B)= 0.15
P(B/A)≠P(B) ⇒ A and B are not independent.
c.
A: "the individual is color-blind" ⇒ P(A)= 0.10
B: "the individual is male" ⇒ P(B)= 0.52
P(A∩B)= 0.08
P(A/B)≠P(A) ⇒ A and B are not independent.
d.
A:"The student received an A in Chemistry" ⇒ P(A)= 0.20
B:"The student received an A in Biology" ⇒ P(B)= 0.25
P(A∩B)= 0.05
P(A/B)= P(A) ⇒ A and B are independent.
I hope it helps!
Ответ:
I hope you have a horrid day.
Step-by-step explanation:
April Fools, Thanks mate, have a superb day