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Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a spade and the ,without replacement, a red card? Express your answer as a fraction or a decimal number rounded to four decimal places

Answer :

Answer:

1/8

Explanation:

Number of spades in a deck of cards = 13

Number of red cards in a deck of cards = 26

Total number of cards in a deck of cards = 52

So the probability of choosing a spade is;

[tex]P(Spade)=\frac{13}{52}[/tex]

After choosing the first card without replacing it, the total number of cards left will be 51, so the probability of choosing a red from 51 cards will be;

[tex]P(Red\text{ card})=\frac{26}{52}[/tex]

So the probability of choosing a spade and then, without replacement, a red card will be;

[tex]\begin{gathered} P(spade\text{ and then red card\rparen}=\frac{13}{52}*\frac{26}{52} \\ =\frac{1}{4}*\frac{1}{2} \\ =\frac{1}{8} \end{gathered}[/tex]

The probability of choosing a spade and then, without replacement, a red card is 1/8

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