Question

A card is drawn and replaced four times from an ordinary pack of $52$ playing cards. The probability that at least once heart is drawn

• A. $(\frac{3}{4}{)}^4$
• B. $1-(\frac{1}{2}{)}^4$
• C. $1-(\frac{3}{4}{)}^4$
• D. $(\frac{1}{2}{)}^4$

Answer 1

The correct option is C $1-(\frac{3}{4}{)}^4$

Probability when one card drawn from a card pack of $52$ and not a heart is $=1-\frac{13}{52}=\frac{3}{4}$; (There are $13$ spade cards in a pack of $52$ cards)
Probability of atleast one heart is drawn $=$ 1 $-$ Probability that none of the four is heart
$=1-(\frac{3}{4}{)}^4$