Question

I'm sorry. I'm not sure if there is a as my question limit, but I have an exam Monday and just trying to clarify some questions.

So, please explain Conditional probability. The definition I got says " the probability the event A will occur GIVEN that event B had occurred." What does that mean?

Suppose that two cards are drawn. What is the probability that the second card drawn is a king, given that the first card was a queen?

Answer 1

What is the probability that a king is drawn, given that a king has already been drawn?

Answer 2

spose we know that given a rainy day, it is more likely that you will have a headache then if it is a sunny day ... the probability of a headache changes based on a particular given event right?

Answer 3

given some circumstance, we can rule our a certain portion of our sample space that simply does not pertain to the situation.

Answer 4

Isnt a headache and the change of weather both independent?

Answer 5

if we look at it from a venn diagram perspective ...



now given event B ... the probability of event occuring within B is just a simple probability calcuation:\[\frac{P(desired~event)}{P(sample~space)}=\frac{P(AnB)}{P(B)}=P(A|B)\]

Answer 6

independence means that the probability of an event is the same for all given sample spaces it occurs in. therefore its probability is independant (does not depend) on a given space since it is the same for all spaces.

Answer 7

sorry, im a slow reader.

Answer 8

if the probability of event A is the same in the universal sample, and also the same within the sample of B ... then the probability of A remains the same regardless of what happens. that is notion of independence.

Answer 9

if the probability of an event changes with respect to a given sample space ... the the probabilty of that event occuring depends upon a given space.

Answer 10

say the probabilty of having a headache for any day of the week is .36

and with some research we can determine that on any given wednesday that the probabilty of having a headache is .42

does the probabilty of having a headache depend on a given event occuring or not?

Answer 11

ooooh, ok. it is starting to click.

Answer 12

so in mathy terms:
\[if~P(A)=P(A|B),~then~P(A)\text{ is independant - it is the same regardless of a given event}\]

Answer 13

... of a given event

Answer 14

Suppose that two cards are drawn. What is the probability that the second card drawn is a king, given that the first card was a queen?

given that the card removed from the deck is a queen.. how many kings are left, and how many cards are left to choose from?

Answer 15

i dont know.

Answer 16

the question of course presupposes that you know what a deck of cards looks like

Answer 17

No, i dont have any knowledge about a deck of cards.

Answer 18

i know there are 52 cards thats it

Answer 19

in general

52 cards in a deck, 4 of then are kings

remove 1 cards that that is not a king leaves us with 51 cards and 4 kings

how do we calculate a basic probabilty?

Answer 20

if you are given a deck of 51 cards that has 4 kings .. whats the probabilty of drawing a king?

Answer 21

soooo...dang it

Answer 22

i am confused now

Answer 23

4 out of 51 ... right?

4/51

Answer 24

why 51?

Answer 25

because given that you pulled out a card ... it is no longer a part of the deck.