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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

Sagot :

Answer:

[tex]0.000495[/tex]

Step-by-step explanation:

Probability refers to chances of occurrence of any event.

Value of probability varies from [tex]0[/tex] to [tex]1[/tex]

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 = [tex]\frac{C(13,5)}{C(52,5)}[/tex]

Use [tex]C(n,r)=\frac{n1}{r!(n-r)!}[/tex]

So,

[tex]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[/tex]

[tex]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[/tex]

Therefore,

Probability that the hand contains 5 spades = [tex]\frac{1287}{2598960}=0.000495[/tex]

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