Two cards are drawn with replacement from a standard deck of 52 playing cards. Find the probability that the first card is a king and the second is a diamond.

Question

amistre64 · Answer

how many kings are in a deck?

how many diamonds are in a deck?

paradise · Answer

Its doesn't say

amistre64 · Answer

these questions assume you know how a deck of cards looks like

amistre64 · Answer

normally:

there are 4 suits in a deck of cards,  hearts, diamonds, spades, and clubs

52/4 = 13 cards in each suit,  so 13 diamonds out of 52 cards

each suit has numbered cards and face cards:  ace, 2, 3, 4, 5, 6, 7, 8, 9, jack, queen, king

since there are 4 suits, and each suit has a king;  there are 4 kings out of 52 cards

amistre64 · Answer

the next question is:  how do you solve a probability question that asks for an "AND" relationship

paradise · Answer

Would you have to add them together?

paradise · Answer

(4/52)(13/52) + (13/52)(4/52) like that?

amistre64 · Answer

thats not quite correct, but a good effort.

the textbooks give us:$$P(AnB)=P(A)*P(B)$$
so that would be multiply them together

amistre64 · Answer

$$P(king)=\frac{4}{52}=\frac1{13}$$
$$P(diamond)=\frac{13}{52}=\frac1{4}$$
$$P(knd)=\frac1{13}*\frac14$$