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!

dunno

step-by-step explanation:

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.