<p>One ticket is selected at random from 50 tickets numbered 00, 01, 02, …, 49. Then the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero, is</p>
Step-by-Step Solution
Key Concept: Use conditional probability formula P(A|B) = P(A∩B)/P(B), where A is 'sum of digits = 8' and B is 'product of digits = 0'. The product is zero only when at least one digit is 0.
<p><strong>Step 1:</strong> Identify all tickets where product of digits = 0 (i.e., at least one digit is 0).</p><p>These are tickets: 00, 01, 02, ..., 09 (10 tickets with first digit 0) and 10, 20, 30, 40 (4 tickets with second digit 0).</p><p>Total: 14 tickets with product of digits = 0.</p><p><strong>Step 2:</strong> Among these 14 tickets, find which have sum of digits = 8.</p><p>From 00-09: Only ticket 08 has sum = 0+8 = 8 ✓</p><p>From 10, 20, 30, 40: Tickets 10, 20, 30, 40 have sums 1, 2, 3, 4 respectively (none equal 8) ✗</p><p>So only 1 ticket satisfies both conditions: sum = 8 AND product = 0.</p><p><strong>Step 3:</strong> Apply conditional probability formula:</p><p>P(sum = 8 | product = 0) = (Number of favorable outcomes)/(Total outcomes with product = 0) = 1/14</p><p>∴ Answer: <strong>1/14</strong></p>
Correct Answer: A