Question

In the word EDUCATION, find the probability of getting a vowel, if a letter is chosen at random from it.
$
  A.\dfrac{1}{9} \\
  B.\dfrac{2}{9} \\
  C.\dfrac{4}{9} \\
  D.\dfrac{5}{9} \\
$

Answer 1

Hint: In order to get this problem solved we need to know the number of vowels present in the word EDUCATION. Vowels are A, E, I, O, U. After that we have to use combinations and select the number of ways. Then we have to apply the formula of probability to get the right answer.

Complete step by step answer:
The word provided to us is EDUCATION.
We need to find the probability of getting a vowel if a letter is chosen at random.
We know that there are 5 vowels and 21 consonants.
The 5 vowels are A, E, I, O, U.
The total number of words present in the word EDUCATION is 9. In which E, U, A, I, O are vowels.
So there are 5 vowels among 9 alphabets.
So, the probability will be the number of favorable outcomes upon total number of outcomes.
Total number of outcomes will be selecting 1 letter from 9 letters present that is $^9{C_1}$.
Number of favorable outcomes is the selection of 1 letter from 5 letters that is $^5{C_1}$.
Therefore the probability of getting the vowel in the word EDUCATION is $\dfrac{{^5{C_1}}}{{^9{C_1}}} = \dfrac{5}{9}$.
Hence, the correct option is D.

Note: When you get to solve such problems you need to know that probability is the number of favorable outcomes upon total number of outcomes. You also need to know that there are 5 vowels and 21 consonants out of 26 letters in English. Those 5 vowels are A, E, I, O, U and any one of those if used in a word than those letters are considered as vowels.