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

The answer on Plato is 40 percent!

Explanation:

Answer 2

`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`