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The card game of Euchre employs a deck that consists of all four of each of the aces, kings, queens, jacks, tens, and nines (one of each suit—clubs, diamonds, spades, and hearts). (a) Find the probability that a randomly selected card from a Euchre deck is a jack (J). (Enter the fraction without reduction on the left hand side of "=" symbol and the final answer on the right hand side reduced to the lowest possible fraction.) (b) Find the probability that a randomly selected card from a Euchre deck is a spade (S). (Enter the fraction without reduction on the left hand side of "=" symbol and the final answer on the right hand side reduced to the lowest possible fraction.)

Respuesta :

The deck is composed of 24 cards. Each value appears four times (4 aces, 4 kings, 4 queens, 4 jacks, 4 tens and 4 nines) and each suit appears six times (for each suit we have the nine, the ten, the jack, queen, king and ace).

Since there are 4 jacks out of 24 cards, the probability of picking a jack is

[tex]\dfrac{4}{24}=\dfrac{1}{6}[/tex]

Since there are 6 spades out of 24 cards, the probability of picking a spade is

[tex]\dfrac{6}{24}=\dfrac{1}{4}[/tex]

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