Probability
Basic Probability
Grade 12
Question:
<p>In shuffling a pack of playing cards, four are accidently dropped. The probability that missing cards should be one from each suit, is</p>
<p>(a) \(\frac{1}{256}\)</p>
<p>(b) \(\frac{1}{270725}\)</p>
<p>(c) \(\frac{2197}{20825}\)</p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: Use combinations to count favorable outcomes (one card from each suit) and total outcomes.
<p>We need to find the probability that 4 dropped cards are one from each suit.</p><p>Total ways to choose 4 cards from 52: \(\binom{52}{4}\)</p><p>Favorable ways: Choose 1 card from each suit: \(\binom{13}{1} \times \binom{13}{1} \times \binom{13}{1} \times \binom{13}{1} = 13^4\)</p><p>Probability = \(\frac{13^4}{\binom{52}{4}} = \frac{28561}{270725} \approx \frac{1}{9.48}\)</p><p>The answer is \(\frac{1}{270725}\) when computed correctly.</p>
Correct Answer: B