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A letter is chosen at random from the word STATISTICS, and another letter is chosen at random from the word ASSISTANT. What is the probability that both letters are the same?
- 1/45
- 13/90
- 19/90
- 5/18
Correct answer: 19/90
Solution
STATISTICS: S(3), T(3), A(1), I(2), C(1) — total 10. ASSISTANT: A(3), S(3), I(2), T(1), N(1) — total 9. P(same) = (3/10)(3/9) + (3/10)(1/9) + (1/10)(3/9) + (2/10)(2/9) = 9/90 + 3/90 + 3/90 + 4/90 = 19/90.
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