Probability of Drawing Two Red Hearts Without Replacement (GED Math)

Calculating Probability Without Replacement

• 🎯 The problem asks for the probability of drawing two red hearts consecutively from a standard 52-card deck without putting the first card back.
• 💡 Understanding the composition of a standard deck is key: 52 total cards, with 13 red hearts.

Probability of the First Draw

• 🃏 For the first draw, there are 13 red hearts out of a total of 52 cards.
• 📈 The probability of drawing a red heart on the first try is therefore 13/52.

Probability of the Second Draw

• ⚠️ Since the first card is not replaced, there are now only 51 cards left in the deck.
• 💔 If the first card drawn was a red heart, there are now only 12 red hearts remaining.
• 📉 The probability of drawing a second red heart, given the first was a red heart, is 12/51.

Final Probability Calculation

• 🧮 To find the probability of both events happening, we multiply the probabilities of each draw: (13/52) * (12/51).
• 🔍 Simplifying the fractions: (13/52) simplifies to 1/4, and (12/51) simplifies to 4/17.
• ✅ Multiplying the simplified fractions (1/4) * (4/17) results in 4/68, which further simplifies to 1/17.
• 🏆 The final probability of drawing two red hearts without replacement is 1 out of 17.