Question

A card is drawn from a well-shuffled standard deck of 52 cards.
a) what is the probability that it is a spade?
b) Probability that it is a king?
c) Probability that it is a king of spades?
are the events in part a and b independent?

Answer 1

a) 1/4 or 25%
b) 4/52 or about 7.6%
c) 1/52 or 1.9%
they are independent

Answer 2

Almost had it typed out, but yes.

Answer 3

@DanielLions do you understand the answers that @ayubie gave?

Answer 4

@SpoonyBard Idk anything about cards, so no.

Answer 5

There are 13 cards for each of the four suits. So, 13 out of the 52 are either spades, clubs, hearts, or diamonds. 13/52 is simplified to 1/4

There are only 4 kings because there is one king for each suit. 4/52 of the cards are kings.

There are only 4 kings, and only one of those kings are spades, so there is only 1/52

Answer 6

Do you understand now?

Answer 7

I think we should show how we know them to be independent also @OrangeMaster

Answer 8

@OrangeMaster yes and @SpoonyBard please.

Answer 9

do you know the definition of independence in probability?

Answer 10

yes @SpoonyBard

Answer 11

ok, then we can use bayes' rule to see if it fits the definition.
Let \(P(S)\) be the probability of drawing a spade, and \(P(K)\) be the probability of drawing a king\[P(S\cap K)=P(S)P(K|S)\]we already have \(P(S)\), can you figure out the probability of drawing a king given that it is a spade?, i.e. \(P(K|S)\)

Answer 12

sorry, not bayes' rule, the multiplication rule*

Answer 13

or, as an equivalent question on an intuitive level, does knowing the suit tell us anything about the odds of drawing a king?