Q.A letter is taken at random from the letters of the word 'ASSISTANT' and another letter is taken at random from the letters of the word 'STATISTICS'. Find probability that the selected letters are the same.

ASSISTANT (9 letters): A(2),S(3),I(1),T(2),N(1). STATISTICS (10 letters): S(3),T(3),A(1),I(2),C(1). The letters common to both words are A, S, I, T. $$P(\text{same})=\frac{2}{9}\cdot\frac{1}{10}+\frac{3}{9}\cdot\frac{3}{10}+\frac{1}{9}\cdot\f …

Treat each letter draw as picking a letter-instance uniformly from that word, sum the product of matching-letter probabilities over every letter common t …

Forgetting to include ALL four shared letters (A, S, I, T) in the sum, or miscounting a let …