Question

Suppose you have a pack of $52$ cards. In $12$ attempts, you pick a red card $5$ times. Find the relative frequency for picking the red card.

Also, find the probability $\text{P(B)}$ of drawing a black card.

• A. $\text{Relative frequency for the red card}$ $=\frac{5}{12}$
  
  $\text{P(B)}=\frac{1}{2}$
  
• B. $\text{Relative frequency for the red card}$ $=\frac{12}{5}$
  
  $\text{P(B)}=\frac{1}{2}$
  
• C. $\text{Relative frequency for the red card}$ $=\frac{5}{12}$
  
  $\text{P(B)}=\frac{1}{3}$
  
• D. $\text{Relative frequency for the red card}$ $=\frac{5}{12}$
  
  $\text{P(B)}=\frac{1}{4}$
  

Answer 1

The correct option is A $\text{Relative frequency for the red card}$ $=\frac{5}{12}$


$\text{P(B)}=\frac{1}{2}$

We are given that out of $12$ trials, red card got picked up only $5$ times.

To find the relative frequency for the red card, we need two data sets:
$\bullet$ Number of times red card actually got picked up, i.e., $5$.
$\bullet$ Total trials done for picking up the card, i.e., $12$.

$\text{Relative frequency for the red card}$ $=\frac{\text{Number of times red card actually got picked up}}{\text{Total trials done for picking up the card}}$

$=\frac{5}{12}$

In a pack of $52$ cards, $26$ cards are of red color and $26$ cards are of black color.

$\text{P(B)}$ denotes the probability of drawing a black card.

Then,
$\text{P(B)}=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Number of favorable outcomes $=26$
Total number of outcomes $=52$

$\text{P(B)}=\frac{26}{52}$

$\text{P(B)}=\frac{1}{2}$



The relative frequency for the red card is $\frac{5}{12}$ and the probability of drawing a black card is $\frac{1}{2}$.


Therefore, option (a.) is the correct answer.