Question

question 2 of 10
on the planet kudzu, the probability that a bird is green is 0.30. the probability that the bird is green given that the bird is female is 0.30.
which statement is true?
a. on kudzu, being female and being green are independent events.
b. on kudzu, being female and being green are dependent events.
c. all of the female birds on kudzu are green.
d. the probability that a bird on kudzu is female and green is 0.30.

Explanation:

Step1: Recall the formula for independent events

Two events \(A\) (bird is green) and \(B\) (bird is female) are independent if \(P(A|B)=P(A)\).

Step2: Substitute the given values

Given \(P(A) = 0.30\) (probability that a bird is green) and \(P(A|B)=0.30\) (probability that the bird is green given that the bird is female).
Since \(P(A|B)=P(A) = 0.30\), by the definition of independent events, being female (\(B\)) and being green (\(A\)) are independent events.

Step3: Analyze other options

• Option B: Incorrect because \(P(A|B)=P(A)\) shows independence, not dependence.
• Option C: \(P(A|B) = 0.30

eq1\), so not all female birds are green.

• Option D: If independent, \(P(A\cap B)=P(A)\times P(B)\). But we are not given \(P(B)\) (probability of a bird being female) to calculate \(P(A\cap B)\). And just because \(P(A|B) = P(A)\) doesn't mean \(P(A\cap B)=0.30\) (unless \(P(B) = 1\), which is not indicated).

Answer:

A. On Kudzu, being female and being green are independent events.