Multiple choice

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

  1. $(\displaystyle \frac{3}{4})^{4}$
  2. $1-(\displaystyle \frac{1}{2})^{4}$
  3. $1-(\displaystyle \frac{3}{4})^{4}$
  4. $(\displaystyle \frac{1}{2})^{4}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of drawing a heart is 1/4, so the probability of not drawing a heart is 3/4. The probability of not drawing a heart in 4 trials is (3/4)^4. The probability of drawing at least one heart is 1 - (3/4)^4.

AI explanation

The probability of drawing a heart is 13/52, which is 1/4. It is easier to find the probability of at least one heart by subtracting the probability of drawing no hearts from 1. The probability of not drawing a heart in one trial is 3/4, so for four independent trials it is (3/4)^4. Therefore, the required probability is 1 minus (3/4)^4.

Keep practicing — related questions