Question

please help me to understand independent events in probability

Answer 1

A and B are said to be independent, if the occurrence of event A does not affect the probability of event B. Knowing that A has already occurred does not affect probability of B.

The classic example is drawing cards with replacement and without replacement. if I ask you, what is probability of drawing two ace's from a 52 card deck, two different cases. with replacement : without replacement:

Answer 2

ok so far?

Answer 3

Probability ( draw two aces with replacement) = 4/52 * 4/52

Probability ( draw 2 aces without replacement) = 4/52 * 3/51

Answer 4

ya... i understand ... , so does event A have to occur first then event B ??

Answer 5

in this example, yes it is assumed.
maybe i can do an easier example.

if you throw two dice, the probability of getting 3 on both throws.
A = getting 3 on first throw
B = getting 3 on second throw.

B is independent of A , since if A occured (you got a 3 on first throw), it doesnt affect probability of getting a 3 on second throw of die

Answer 6

ya..but this example see

find the probabilty of choosing a red face card from a deck of card ??

is = P(choosing red card) *P(choosing face card )

how r those two events independent ?

Answer 7

if P(B |A ) = P(B) , then we say B is 'independent' of A

P(B | A ) means probability of B *given* that you know A has occurred.

P(B) means probability of B where you don't know if A has or has not occurred (unconditional probability)

Answer 8

the example has to say whether you are replacing the card or not, back to the deck

Answer 9

ur taking only 1 card there a red-face card

Answer 10

for just one card, it doesnt make sense to say independent. usually you need two events

Answer 11

some event is independent of another event. the statement is a relational statement, like x is taller than y , A is independent of B . you need two things to discuss independence

Answer 12

oh...

Answer 13

in your example, P ( choosing red face card ) is just the probability of choosing one red face card. there is no independence in this event by itself

Answer 14

but if you said, find probability of drawing two red face cards, which is equal to the probability of drawing one red face card *followed* by drawing another red face card... then the events would be independent or dependent based on whether you are drawing with or without replacement

Answer 15

thank you :)