Question

P(A) = 0.63, P(B) = 0.41, and P(B | A) = 0.41. Are the events independent? Justify mathematically.

Yes, because 0.41 = 0.41
No, because 0.63 ≠ 0.41
Yes, because 0.63 ≠ 0.41
No, because 0.41 = 0.41

Answer 1

I believe its B @jayfafr (Sorry for all the pings but thank you for your help!)

Answer 2

Events A and B are independent if and only if P(B|A) = P(B).

Given in the problem:
P(B) = 0.41
P(B|A) = 0.41

Since P(B|A) is equal to P(B), the events are independent.

The correct answer is:

Yes, because 0.41 = 0.41

Answer 3

yea I don't mind

Answer 4

not doing anything rn anyway lol

Answer 5

Yes, because
0.41
=
0.41
0.41=0.41

Answer 6

Thank you guys

Answer 7

anytime!