Probability
Classical Probability
Grade 12
Question:
<p>There are 5 pairs of shoes in a shoe rack. Four shoes are drawn one by one at random then-</p>
<p>(a) probability that at least one pair of shoes is drawn is 13/21</p>
<p>(b) probability that at least one pair of shoes is drawn is 11/21</p>
<p>(c) probability that at no pair of shoes is drawn is 10/21</p>
<p>(d) probability that at no pair of shoes is drawn is 8/21</p>
Step-by-Step Solution
Key Concept: Use complementary counting: find the probability that at least one complete pair is formed, then subtract from 1. Alternatively, count favorable outcomes where NO complete pair exists by tracking which shoes can be selected.
<p><strong>Step 1:</strong> Total ways to draw 4 shoes from 10 shoes = C(10,4) = 210</p><p><strong>Step 2:</strong> For NO complete pair to be formed, the 4 shoes must come from at most 4 different pairs (and none can have both shoes from the same pair).</p><p><strong>Step 3:</strong> Ways to select shoes with NO complete pair: Choose 4 pairs from 5 [C(5,4)=5], then choose 1 shoe from each selected pair [2⁴=16]. Total = 5 × 16 = 80</p><p><strong>Step 4:</strong> Ways to get AT LEAST ONE complete pair = 210 - 80 = 130</p><p><strong>Step 5:</strong> Probability = 130/210 = 13/21</p><p>∴ Answer: AC (probability is 13/21 or approximately 0.619)</p>
Correct Answer: AC