Question

A letter is taken out at random from the word RANGE and another is taken out from the word PAGE. The probability that they are the same letter is

• A. $\frac{3}{5}$
• B. $\frac{3}{4}$
• C. $\frac{1}{20}$
• D. $\frac{3}{20}$

Answer 1

Answer: (D)

$\frac{3}{20}$

A letter from the word RANGE can be taken out in $5$ ways. Similarly, a letter from the word PAGE can be taken out in $4$ ways.
So, both the task of taking one letter from each word can be done in $5\ast 4=20$ ways.
We have to find the probability that both the letter are the same.
The words RANGE and PAGE have $3$ letters in common: A, G and E.
So a common letter can be chosen in $3$ different ways, and once chosen from any one word then we have only $1$ choice of taking out a letter from the other word.
So, favorable number of ways $=3\ast 1=3$
Prabability $=$ $\frac{favorableno.ofways}{totalno.ofways}$
$=$ $\frac{3}{20}$