Question

Three cards are randomly selected from a standard 52-card deck, one at a time, with each card re- placed in the deck before the next one is picked. Find the probability of all three cards are hearts.

Answer 1

Answer:

$\frac{1}{4}$

Step-by-step explanation:

Three cards are randomly selected from a standard 52-card deck.

Number of heart cards in a deck = 13

Each card replaced in the deck before the next one is picked.

Probability of first card is heart = $P_{1}=\frac{13}{52}$

After replacement, the probability of second card is heart = $P_{2}=\frac{13}{52}$

after replacement, the probability of third card is heart =  $P_{3}=\frac{13}{52}$

P =  $\frac{13}{52}$ ×  $\frac{13}{52}$ ×  $\frac{13}{52}$

  =  $\frac{39}{156}$

  =  $\frac{1}{4}$

The probability of all three cards are hearts is  $\frac{1}{4}$