Question

P(A) = 0.41, P(B) = 0.2, and P(A|B) = 0.2. Are the events independent? Justify mathematically.

Yes, because 0.2 = 0.2
No, because 0.2 ≠ 0.41
Yes, because 0.2 ≠ 0.41
No, because 0.2 = 0.2

Answer 1

@toga

Answer 2

I'll say Yes, because 0.2 = 0.2

Answer 3

Let's see if it's righttt

Answer 4

I hope it is right

Answer 5

No, the events are not independent because the conditional probability of A given B, P(A|B), is not equal to the marginal probability of A, P(A). Mathematically, if two events A and B are independent, then P(A|B) should be equal to P(A). However, in this case, P(A|B) = 0.2 and P(A) = 0.41, which means that the occurrence of event B affects the probability of event A. Therefore, we can conclude that events A and B are dependent.

Answer 6

....sniffles I'ma retake it..

Answer 7

No no I'ts fine, so because I'm dumb dumb its B right?

Answer 8

Welp sorry baby I wasn't really sure

Answer 9

The correct answer is (c) Yes, because 0.2 ≠ 0.41.

Two events A and B are said to be independent if and only if P(A|B) = P(A).

In this case, P(A) = 0.41, P(B) = 0.2, and P(A|B) = 0.2.

If A and B were independent, then P(A|B) = P(A), but since P(A|B) ≠ P(A), we can conclude that A and B are not independent. Therefore, option (c) is the correct answer.

Answer 10

Ohhh right because it's asking if their independent.

Answer 11

I get it now