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Problem 7. 20 pts Kirk, Spock, Uhura, and Scotty are playing a game of cards. They shuffle a complete deck of 52 cards and then distribute all the cards evenly among themselves. Given that each of them gets an ace, what is the probability that Kirk has the ace of spades?

Respuesta :

Answer: Our required probability would be [tex]\dfrac{1}{4}[/tex]

Step-by-step explanation:

Since we have given that

Let A be the event that Kirk has the ace of spades.

Let B be the event that everyone has an ace.

So, P(A)  = [tex]\dfrac{1}{52}[/tex]

P(B) = [tex]\dfrac{4}{52}[/tex]

And P(A∩B) = [tex]\dfrac{1}{52}[/tex]

So, P(Kirk has the ace of spades | each of them gets an ace)

[tex]\dfrac{P(A\cap B)}{P(B)}\\\\\\=\dfrac{\dfrac{1}{52}}{\dfrac{4}{52}}\\\\\\=\dfrac{1}{4}[/tex]

Hence, our required probability would be [tex]\dfrac{1}{4}[/tex]

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