Question

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 1

1/8

Step-by-step 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;

`P(Spade)=(13)/(52)`

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;

`P(Red\text{ card})=(26)/(52)`

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

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

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