Subtopic: Mean, median, mode and standard deviation
Question Statement:
Two cards are drawn in succession (without replacement) from a pack of red cards only (26 cards). The probability of drawing a king first, followed by a queen, is P×10⁻³. Find P. (Rounded to 3 decimal places)
Official Answer Key:
6.100 to 6.200
Step-by-Step Solution & Explanation
• **Concept:** Probability of drawing dependent successive events without replacement from a reduced sample space.
• **Given:** Pack of red cards only (26 total red cards: 13 Hearts and 13 Diamonds).
- Number of Kings in red deck = 2 (King of Hearts, King of Diamonds).
- Number of Queens in red deck = 2 (Queen of Hearts, Queen of Diamonds).
• **Probabilities:**
- Probability of 1st card being a King: $P(K_1) = \frac{2}{26}$.
- Since the king is not replaced, 25 cards remain, of which 2 are queens.
- Probability of 2nd card being a Queen: $P(Q_2 | K_1) = \frac{2}{25}$.
• **Combined Probability:**
$P = \frac{2}{26} \times \frac{2}{25} = \frac{4}{650} = \frac{2}{325} \approx 0.0061538$
• **Reported Numerical Format:** Expressed in parts per thousand ($10^{-3}$ basis): $0.0061538 \times 1000 = 6.154$ (or $0.615\%$).
• **Conclusion:** Value is $6.154$ (Official range: 6.100 to 6.200).
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.