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

Answer: (C)

$\frac{19}{90}$

The common letters are $A,S,T,I$
$P\left(S\right)=\frac{3}{9}\times \frac{3}{10}$

$P\left(A\right)=\frac{2}{9}\times \frac{1}{10}$

$P\left(T\right)=\frac{2}{9}\times \frac{3}{10}$

$P\left(I\right)=\frac{1}{9}\times \frac{2}{10}$
$\Rightarrow P=P\left(A\right)+P\left(S\right)+P\left(T\right)+P\left(I\right)=\frac{9}{90}$