Question

A letter is taken out at random from the word ASSISTANT and an other from STATISTICS. The probability that they are the same letters is :

• A. $\frac{13}{90}$
• B. $\frac{17}{90}$
• C. $\frac{19}{90}$
• D. $\frac{15}{90}$

Answer 1

The correct option is C $\frac{19}{90}$

The probability that A is taken out from first word = $\frac{2}{9}$

The probability that A is taken out from second word = $\frac{1}{10}$

$\to$ Probability that A is taken out from both words = $\frac{2}{9}\times \frac{1}{10}=\frac{2}{90}$

Similarly ,

Probability that S is taken out from both words = $\frac{3}{9}\times \frac{3}{10}=\frac{9}{90}$

Probability that I is taken out from both words = $\frac{1}{9}\times \frac{2}{10}=\frac{2}{90}$

Probability that T is taken out from both words = $\frac{2}{9}\times \frac{3}{10}=\frac{6}{90}$

Probability that same letters are taken out = $\frac{2}{90}+\frac{9}{90}+\frac{2}{90}+\frac{6}{90}=\frac{19}{90}$