Question

g Five cards (a hand) are dealt from a randomly shuffled deck of cards. For those of you that are not familiar with playing cards: each card has a suit (hearts, spades, diamonds, clubs) and a symbol (aces, kings, queens, etc.). The deck contains a total of 52 cards, with 13 of each suit and 4 of each symbol. What is the probability that the hand contains a) all spades

Answer 1

Answer:

$0.000495$

Step-by-step explanation:

Probability refers to chances of occurrence of any event.

Value of probability varies from $0$ to $1$

Probability = Number of favorable outcomes ÷ Total number of outcomes

Total number of cards = 52

Number of spades = 13

Probability that the hand contains 5 spades = $\frac{C(13,5)}{C(52,5)}$

Use $C(n,r)=\frac{n1}{r!(n-r)!}$

So,

$C(13,5)=\frac{13!}{5!(13-5)!}=\frac{13!}{5!8!}=\frac{13(12)(11)(10)(9)8!}{5(4)(3)(2)(1)8!} =1287$

$C(52,5)=\frac{52!}{5!(52-5)!} =\frac{52!}{5!47!}=\frac{52(51)(50)(49)(48)47!}{5(4)(3)(2)(1)47!}= 2598960$

Therefore,

Probability that the hand contains 5 spades = $\frac{1287}{2598960}=0.000495$