<p>One ticket is selected at random from 100 tickets numbered 00, 01, 02, ..., 99. Suppose \(A\) and \(B\) are the sum and product of the digit found on the ticket, respectively. Then \(P((A = 7)/(B = 0))\) is given by</p>
Step-by-Step Solution
Key Concept: Use the conditional probability formula P(A|B) = P(A∩B)/P(B). First identify all tickets where B=0 (product of digits is 0), then among those, count how many have A=7 (sum of digits is 7).
<p><strong>Step 1:</strong> Find all tickets where B = 0 (product of digits = 0).</p><p>Product is 0 when at least one digit is 0. These tickets are: 00, 01, 02, ..., 09 (10 tickets) and 10, 20, 30, ..., 90 (9 tickets). Total: 19 tickets.</p><p><strong>Step 2:</strong> Among these 19 tickets, find which ones have A = 7 (sum of digits = 7).</p><p>From first group (0_): 07 has sum 0+7=7 ✓</p><p>From second group (_0): 70 has sum 7+0=7 ✓</p><p>So 2 tickets satisfy both A=7 and B=0.</p><p><strong>Step 3:</strong> Apply conditional probability formula.</p><p>P(A=7|B=0) = (Number of tickets with A=7 AND B=0) / (Number of tickets with B=0)</p><p>P(A=7|B=0) = 2/19</p><p>∴ Answer: A</p>
Correct Answer: A