Question

A standard deck of cards is shuffled. What is the probability of:

• A. $P\left(RedFace\right)=\frac{4}{13}$
  $P\left(Black\right)=\frac{1}{2}$
• B. $P\left(RedFace\right)=\frac{3}{26}$
  $P\left(Black\right)=\frac{1}{2}$
• C. $P\left(RedFace\right)=\frac{1}{2}$
  $P\left(Black\right)=\frac{1}{4}$
• D. $P\left(RedFace\right)=\frac{1}{4}$
  $P\left(Black\right)=\frac{1}{4}$

Answer 1

The correct option is B $P\left(RedFace\right)=\frac{3}{26}$

$P\left(Black\right)=\frac{1}{2}$
Number of red cards$=26$
Number of red face cards$=3\times 2=6$

Number of black cards $=26$
Total number of cards $=52$
Therefore,
$P\left(Redfacecard\right)=\frac{6}{52}=\frac{3}{26}$
$P\left(Black\right)=\frac{26}{52}=\frac{1}{2}$