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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

User Yugandhar Pathi
by
3.0k points

2 Answers

8 votes
8 votes

Answer:

The answer on Plato is 40 percent!

Explanation:

User Chad N B
by
2.4k points
22 votes
22 votes

Answer:


0.000495

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 =
(C(13,5))/(C(52,5))

Use
C(n,r)=(n1)/(r!(n-r)!)

So,


C(13,5)=(13!)/(5!(13-5)!)=(13!)/(5!8!)=(13(12)(11)(10)(9)8!)/(5(4)(3)(2)(1)8!) =1287


C(52,5)=(52!)/(5!(52-5)!) =(52!)/(5!47!)=(52(51)(50)(49)(48)47!)/(5(4)(3)(2)(1)47!)= 2598960

Therefore,

Probability that the hand contains 5 spades =
(1287)/(2598960)=0.000495

User Eli Stevens
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2.7k points