Question

A card is drawn at random from a standard deck of cards. Find the probability of drawing:
1. A queen or a spade.
II. A black or a face card.
III. A red queen.

Answer 1

Given that a card is drawn at random from a standard deck of cards. We are asked to find the probabilities of

1) A queen or a spade.

2) A black or a face card.

3) A red queen.

This can be seen below;

Explanation

The formula for the probability of an event is given as;

$\text{Pr(event) =}\frac{\text{number of events}}{\text{number of total possible outcomes}}$

For a given deck of cards, the number of total possible outcomes is 52 different cards. Next, we find the number of events for each case

$\begin{gathered} n(\text{queen)}=4 \\ n(\text{spades)}=13 \\ n(\text{black)}=26 \\ n(\text{face card)=}12 \\ n(\text{red queen) =2} \end{gathered}$

Therefore we can find the probability in each case. Recall that "or" in probability implies we will add the values of the probabilities we are comparing.

1) A queen or a spade

$Pr(\text{queen or spade)= }\frac{4}{52}+\frac{13}{52}=\frac{17}{52}$

Answer

$Pr(\text{queen or spade)=}\frac{17}{52}$

2) A black or a face card

$Pr(black\text{ or }facecard)=\frac{26}{52}+\frac{12}{52}=\frac{38}{52}=\frac{19}{26}$

Answer:

$Pr(\text{black or facecard)=}\frac{\text{19}}{26}$

3) A red queen

$Pr(A\text{ }red\text{ }queen)=\frac{2}{52}=\frac{1}{26}$

Answer

$Pr(A\text{ }red\text{ }queen)=\frac{1}{26}$