Step-by-Step Solution
Key Concept: P(X = Y) requires finding the probability that two random variables take identical values simultaneously. This is computed by summing the joint probabilities P(X = i, Y = i) over all possible values i where both can equal the same number.
<p><strong>Step 1:</strong> Identify all cases where X and Y can be equal. Look at the joint probability table for pairs (i, i) where both variables take the same value.</p><p><strong>Step 2:</strong> Sum the joint probabilities for all such matching pairs: P(X = Y) = P(X = 0, Y = 0) + P(X = 1, Y = 1) + P(X = 2, Y = 2) + ...</p><p><strong>Step 3:</strong> Read each probability from the given joint probability table and add them together.</p><p><strong>Step 4:</strong> Verify your sum is ≤ 1 and simplify if needed.</p><p>∴ Answer: C</p>
Correct Answer: C