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.
Accepted Solution
A:
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 = 13Each 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]