Question

A letter is selected from each of the words $MATHEMATICS$ and $STATISTICS$. The probability that the same letter is selected is $\frac{a}{b}$, then $a+b+3$ (where $a$ and $b$ are co-prime) is divisible by

• A. $3$
• B. $5$
• C. $7$
• D. $13$

Answer 1

Answer: (B), (D)

$5$
$13$

Number of letters in $MATHEMATICS=11$
The probability to choose any one letter $=\frac{1}{11}$
Similarly, the probability to choose any one letter for $SATISTICS$ $=\frac{1}{10}$
Now, the common letters are $A,T,I,C,S$
$\therefore$The probability of choosing same letter $=\frac{2}{11}\times \frac{1}{10}+\frac{2}{11}\times \frac{3}{10}+\frac{1}{11}\times \frac{2}{10}+\frac{1}{11}\times \frac{1}{10}+\frac{1}{11}\times \frac{3}{10}$
$=\frac{14}{110}=\frac{7}{55}$
$\therefore a+b+3=7+55+3=65$