Question

You draw 1 card at random from a well-shuffled deck of 52 cards, set it aside without replacing it, and draw another card from the deck at random. The events "get the king of spades on the first draw" and "get the queen of diamonds on the second draw" are independent events.
True or False???

Answer 1

In probability theory, independence means that the occurrence of one does not affect the probability of the other.
In this case there are two possible alternatives,
-you could draw queen of diamonds on the first card (or not), which would affect the outcome of the second choice. In which case the first event would directly impact the probability of the second event occuring, so I would guess that these event are not independent.

That's how I would take it, maybe someone else could clarify?

Answer 2

so r u saying that its false

Answer 3

@ybarrap

Answer 4

I would say false.

Answer 5

f P(A|B) = P(A), then the events are independent
Let A = getting KS and B = getting QD
You would not expect P(B) = P(B on 2nd draw|A on 1st draw), since P(B) = 1/52, but P(B|A) = 1/51

Answer 6

so... u say true?

Answer 7

False, because the second event is dependent of the 1st event.

Answer 8

oh, right.

Answer 9

If you draw a QD on 1st then P(B on second) = zero, otherwise, it's 1/51

Answer 10

ok.

Answer 11

So P(B on second) is totally dependent on what happens on the 1st draw

Answer 12

True now. Because now P(B on second) is totally independent of what happened on the 1st draw.

Answer 13

True

Answer 14

ok.

Answer 15

how do u do this? :/

Answer 16

@terenzreignz

Answer 17

The intersection \(\cap\) means an 'and' operator.
So you're being asked which hand is in F and in S
F is "all the cards in your hand are the same suit"
and
S is "all the numbers in your card form an uninterrupted sequence"

Do you play poker? :P

Answer 18

no :p

Answer 19

so how can I solve this

Answer 20

Well, that's a pity.
You'll find that the set F is the set of all hands which are 'flushes'
while the set S is the set of all hands which are "straight's"

In effect, the set \(\large F \cap S\) is the set of all straight flushes...

Answer 21

So, which of those hands have cards which all have the same suit?

Answer 22

B

Answer 23

A

Answer 24

D

Answer 25

It had to be in that order?
Besides, C are all spades...

Answer 26

no it doesn't have to be in that order... C is???

Answer 27

C also consists of a hand that are all the same suit... they're all spades...

Answer 28

what abt the Jack?

Answer 29

If you actually read your question, the J = 11, Q = 12, K = 13
:P

Answer 30

yeah I know I mean to say that its a ♥ though

Answer 31

@ybarrap ?

Answer 32

Crud... my eyes fail me....

Answer 33

Apologies, @music101

Answer 34

They really should colour these things :P

Answer 35

oh its fine

Answer 36

A. satisfies both events, suit and uninterrupted sequence. B. does not because there is a suit ther mixed with the hearts that doesn't look like any suit. Why the rest don't satisfy the conditions is obvious.

Answer 37

So, B, A, and D all have five cards with the same suit...
now, among these three, which form an uninterrupted sequence?

Answer 38

what do u mean an uninterrupted sequence

Answer 39

A straight...
err
for example, A,2,3,4,5

or
8,9,10,J,Q
You get the idea :)

Answer 40

so A&B?

Answer 41

That is correct :)

Answer 42

ok :) hope that's correct.. oh btw what did @ ybarrap mean "B is not"