Question

are these independent ???
If P(A) = 0.45, P(B) = 0.25, and P(B|A) = 0.45, are A and B independent?


yes , no , or cannot determine ??

Answer 1

What did you get?

Answer 2

Keep in mind that if two events are independent, then the two events do not alter each others probabilities

Answer 3

i guessed no ?

Answer 4

just a guess or did you have any reason behind that?

Answer 5

it's ok it was just a guess, I'm just curious

Answer 6

im guessing because it didnt take into account p(b) but yeah it could be a bad guess lol

Answer 7

notice how it says P(B) = 0.25

Answer 8

then it says P(B | A) = 0.45

Answer 9

the first thing says that the probability of event B happening is 0.25, or a 25% chance

Answer 10

P(B | A) = 0.45 means that given we know event A has happened, the chances of B happening are 0.45 (or a 45% chance)

so clearly knowing that event A has happened has altered the probability of event B happening

Answer 11

So that shows us that A and B are not independent

Answer 12

if it told us that P(B) = 0.25 and P(B|A) = 0.25, then this would mean that P(B) = P(B|A) and it would tell us that A and B are independent since A didn't change B

but that's not the case here

Answer 13

alternative :
A and B are independent if satisfies :
P(A) * P(B) = P(A and B)

we knowed that :
P(B|A) = P(A and B)/P(A)
so, from here we got
P(A and B) = P(A) * P(B|A) = 0.45 * 0.45 = 0.2025

just check the multiply of P(A) * P(B) is equal 0.2025
P(A) * P(B) = 0.45 * 0.25 not equal 0.025

Answer 14

because P(A) * P(B) not equal P(A and B)
so, it is not independent

Answer 15

thanks guys :)