Question

A card is drawn at random from a deck of playing cards. What is the probability of drawing:

• A. $P\left(\text{Heart Face}\right)=\frac{2}{26}$
  $P\left(\text{Spade > 8}\right)=\frac{2}{13}$
• B. $P\left(\text{Heart Face}\right)=\frac{3}{52}$
  $P\left(\text{Spade > 8}\right)=\frac{1}{26}$
• C. $P\left(\text{Heart Face}\right)=\frac{1}{26}$
  $P\left(\text{Spade > 8}\right)=\frac{3}{52}$
• D. $P\left(\text{Heart Face}\right)=\frac{3}{26}$
  $P\left(\text{Spade > 8}\right)=\frac{3}{13}$

Answer 1

The correct option is B $P\left(\text{Heart Face}\right)=\frac{3}{52}$

$P\left(\text{Spade > 8}\right)=\frac{1}{26}$
Total number of cards $=52$
Total number of face cards $=12$
Number of heart face cards $=3$ namely $\text{{Jack, Queeen, King}}$
Number of spade cards greater than $8$ = $2$ namely $\{9,10\}$

Hence,
$P\left(\text{Heart Face}\right)=\frac{3}{52}$

$P\left(\text{Spade > 8}\right)=\frac{2}{52}=\frac{1}{26}$