Question

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

• A. 1/45
  
• B. 13/90
  
• C. 19/90
  
• D. 5/18

Answer 1

The correct option is C

19/90

Letters of the word $STATISTICS$ are
$AIICSSSTTT$
Letters of the word $ASSISTANT$ are
$AAINSSSTT$
Common letters are A, I, S and T
Probability of choosing A is $\frac{1}{10}\times \frac{2}{9}=\frac{2}{90}$
Probability of choosing I is $\frac{2}{10}\times \frac{1}{9}=\frac{2}{90}$
Probability of choosing S is $\frac{3}{10}\times \frac{3}{9}=\frac{9}{90}$
Probability of choosing T is $\frac{3}{10}\times \frac{2}{9}=\frac{6}{90}$
$\therefore$ Probability of required event= $\frac{2}{90}+\frac{2}{90}+\frac{9}{90}+\frac{6}{90}=\frac{19}{90}$