Answer:
[tex]\frac{1}{4}[/tex]
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 = [tex]P_{1}=\frac{13}{52}[/tex]
After replacement, the probability of second card is heart = [tex]P_{2}=\frac{13}{52}[/tex]
after replacement, the probability of third card is heart = [tex]P_{3}=\frac{13}{52}[/tex]
P = [tex]\frac{13}{52}[/tex] × [tex]\frac{13}{52}[/tex] × [tex]\frac{13}{52}[/tex]
= [tex]\frac{39}{156}[/tex]
= [tex]\frac{1}{4}[/tex]
The probability of all three cards are hearts is [tex]\frac{1}{4}[/tex]
