Question

Consider two events such that P(A) = 1/6, P(B) = 3/5 , and P(A ∩ B) = 2/15. Are events A and B independent events?

A. Yes, they are independent because P(A) ⋅ P(B) = P(A ∩ B)
B. No, they are dependent because P(A) ⋅ P(B) = P(A ∩ B)
C. Yes, they are independent because P(A) ⋅ P(B) ≠ P(A ∩ B)
D. No, they are dependent because P(A) ⋅ P(B) ≠ P(A ∩ B)

Answer 1

i really need help again @mathmale can you help me please?

Answer 2

Memory rusty. So, I did an Internet search on your behalf. Please see:

https://www.wyzant.com/resources/lessons/math/statistics_and_probability/probability/further_concepts_in_probability

Answer 3

As much as I'd like to help further with this, I'm declining. Been a long day for me.

Answer 4

In this case, we judge whether two events are dependent or not by whether "the probability of B happening, given that A has happened) is the SAME as "the probability that B has happened." In other words, A having happened doesn't affect P(B).

Answer 5

The definition of two events being independent: A and B are independent if\[P(A)P(B)=P(A\cap B)\]and if [P(A)P(B)=P(A\cap B)\] then A and B are independent

Answer 6

they are independent events because P(A) and P(B) did not equal P(A n B)

Answer 7

so it must be C

Answer 8

Nono, reread the defintion

Answer 9

If P(A)P(B)=P(AnB), then A and B are independent

Answer 10

so the answer has to be independent right not dependent, either A or C right?

Answer 11

since they do not rely on each other so it can't be dependent @Bobo-i-bo

Answer 12

it didn't say they were independent in the question, it was asking if they are so it is C i think

Answer 13

No :P

Answer 14

then what

Answer 15

i already submitted the answer and got it wrong

Answer 16

As I said, if
\[P(A)P(B)=P(A \cap B)\]
then A and B are independent. Therefore if:
\[P(A)P(B)\neqP(A \cap B) \]
then A and B are not dependent

Answer 17

okay thanks

Answer 18

P(A)P(B)=1/10 which does not equal to P(AnB) so they are not independent, hence they are dependent. Therefore the answer is D.

Answer 19

Lol, sorry I didn't make it in time

Answer 20

awww man and its okay but thank you for helping me, now i get it and can do it myself if i get a question like that again!

Answer 21

^_^