Question

A letter is taken at random from the word "STATISTICS" and another letter is taken at random from the word "ASSISTANT". The probability that they are same letters is

• A. \( \frac{1}{45} \)
• B. \( \frac{13}{90} \)
• C. \( \frac{19}{90} \)
• D. \( \frac{5}{18} \)
• E. \( \frac{9}{10} \)

Hint:

Break probability into cases based on each matching letter.

Answer 1

The Correct Option is B

Concept: Probability of matching letters: \[ \sum P(\text{letter in first}) \times P(\text{same in second}) \]

Step 1: Count letters in "STATISTICS".
Total = 10 letters

Step 2: Count letters in "ASSISTANT".
Total = 9 letters

Step 3: Count frequencies of common letters.
S, T, A, I appear in both words

Step 4: Compute probabilities for each letter and multiply.
Example: \[ P(S) = \frac{3}{10},\quad P(S\text{ in second}) = \frac{3}{9} \] Similarly for all letters and sum contributions.

Step 5: Final sum gives: \[ \frac{13}{90} \]