A standard deck of cards consists of 52 cards. There are 13 cards in each of four suits- clubs, diamonds, hearts and spades. Within each suit, there are 13 denominators- Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King, the last three of which are known as "face cards".
a) we have two shuffled decks of cards and we randomly select one card from each deck. The outcome of interest is the suit of each of the two cards selected. List the sample space.
{
(clubs, clubs), (clubs, diamonds), (clubds, hearts), (clubs, spades),
(diamonds, clubs), (diamonds, diamonds), (diamonds, hearts), (diamonds, spades),
(hearts, clubs), (hearts, diamonds), (hearts, hearts), (hearts, spades),
(spades, clubs), (spades, diamonds), (spades, hearts), (spades, spades)
}
b) Suppose the outcome of interest is the denomination of each of the two selected cards. How many outcomes would be containedin the sample space?
13 x 13 = 169
Ans: 169
c) what is the probability of selecting two face cards?
One card is selected from each deck. For two face cards, one face card is to be selected from each deck.
Number of favorable outcomes = 1
Size of sample space = 169
Probability = 1/169
Ans: 1/169
d) What is the probability that the same suit is selected from each deck?
In answer of part a, there are 4 outcomes which have same suit from each deck.
Number of suits = 4
Total number of possible outcomes = 4 x 4 = 16
Probability = number of favorable outcomes/size of sample space
= 4/16
= 1/4
Ans: 1/4
e) what is the probability of selecting two hearts or two 7's?
P(two hearts) = 1/169
P(two 7's) = 1/169
P(two hearts or two 7's) = 1/169 + 1/169 = 2/169
Ans: 2/169