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.

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!

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.

answer: get jesus in your life

step-by-step explanation: