<p>Since 7 coupons are numbered from 1 to 9 so that '9' is selected at least once, the required probability is:</p>
Step-by-Step Solution
Key Concept: Use complementary probability: P(at least one 9) = 1 - P(no 9s). Since we're selecting from coupons 1-9, we need to identify how many selections occur and calculate the probability that none of them are the coupon numbered 9.
<p><strong>Step 1:</strong> Identify the setup. We have 9 coupons (numbered 1 to 9) and we're making 7 selections (with/without replacement - typically with replacement for such problems).</p><p><strong>Step 2:</strong> Use complementary probability. P(at least one 9) = 1 - P(no 9 in all 7 selections)</p><p><strong>Step 3:</strong> For each selection, probability of NOT getting 9 = 8/9</p><p><strong>Step 4:</strong> For 7 independent selections, P(no 9) = (8/9)^7</p><p><strong>Step 5:</strong> Therefore, P(at least one 9) = 1 - (8/9)^7</p><p><strong>Step 6:</strong> Simplify: = [9^7 - 8^7]/9^7</p><p>∴ Answer: B</p>
Correct Answer: B