In a standard deck of 52 cards, there are 4 suits: clubs, diamonds, hearts and s
ID: 3217336 • Letter: I
Question
In a standard deck of 52 cards, there are 4 suits: clubs, diamonds, hearts and spades. For each suit, there are 13 numbers ranging from A (Ace), 2, 3, . . ., 10, J (Jack), Q (Queen), K (King). In the game Bridge, each player gets 13 cards from a standard deck of 52 cards. What is the probability that
a. all 13 cards have the same suit?
b. the 4 aces are part of the 13 cards?
c. none of the 13 cards have the same number?
d. exactly seven of the 13 cards are spades?
e. at least seven of the 13 cards are spades?
Explanation / Answer
13 cards from a deck of 52 cards can be selected in 52C13 ways
(a) All 13 cards are part of the same suit, this can be done tin 4C1*13C13 ways
Hence probability = 4/52C13
(b)
Four aces can be selected in 1 way and remaining 9 cards can be selected in 48C9 ways
Hence probability = 48C9/52C13 = 0.00264
(d)
7 spades can be selected in 13C7 ways and remaining 6 cards can be selected in 39C6 ways
Hence probability = 39C6*13C7/52C13 = 0.0088
(e)
at least 7 of the 13 cards are spades, 13C7*39C6 + 13C8*39C5 + 13C9*39C4 + 13C10*39C3 + 13C11*39C2 + 13C12*39C1 + 13C13*39C0
Hence probability = (13C7*39C6 + 13C8*39C5 + 13C9*39C4 + 13C10*39C3 + 13C11*39C2 + 13C12*39C1 + 13C13*39C0)/52C13 = 0.0101