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Previous Year Question (PYQs)
3
A letter is taken at random from the letters of the word STATISTICS and another letter is taken at random from the letters of the word ASSISTANT.
The probability that they are the same letter is
Solution
STATISTICS: $S(3),T(3),A(1),I(2)$
ASSISTANT: $S(3),T(2),A(2),I(1),N(1)$
Probability
$=\dfrac{3\cdot3+3\cdot2+1\cdot2+2\cdot1}{10\cdot9}$
$=\dfrac{19}{90}$
Answer: $\boxed{\dfrac{19}{90}}$
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