Question

A card is chosen at random from a standard deck of $52$ playing cards. What is the probability (in percent) of choosing a card that is not a club?

• A. $55\%$
• B. $65\%$
• C. $70\%$
• D. $75\%$

Answer 1

The correct option is D $75\%$

Total number of cards in a standard deck $=52$
Number of clubs in the standard deck $=13$

$\text{P(choosing a club)}=\frac{\text{Number of clubs in the deck}}{\text{Total number of cards in the deck}}$

$\Rightarrow \text{P(choosing a club)}=\frac{13}{52}=\frac{13\times 1}{13\times 4}=\frac{1}{4}$

We know,
$\text{P(not choosing a club)=1-P(choosing a club)}$

$\Rightarrow \text{P(not choosing a club)}=1-\frac{1}{4}$
$\Rightarrow \text{P(not choosing a club)}=\frac{4}{4}-\frac{1}{4}$

$\Rightarrow \text{P(not choosing a club)}=\frac{4-1}{4}=\frac{3}{4}=0.75$

$\Rightarrow \text{P(not choosing a club)}\text{in percent}=0.75\times 100=75\%$

$\therefore$ The probability of NOT choosing a club from a standard deck of $52$ cards is $\frac{3}{4}$ or $75\%$.

Hence, option (d.) is the correct choice.