10th Class Mathematics Probability Question Bank MCQs - Probability

A letter is chosen at random from the Letters of the word 'ASSASSINATION', then the probability that the letter chosen is a vowel is in the form of \[\frac{6}{2x+1},\] then x is equal to:

A) 5

B) 6

C) 7

D) 8

Correct Answer: B

Solution :

[b] There are 13 letters in the word 'ASSASSINATION' out of which one letter can be chosen in 13 ways.

Hence, total number of outcomes =13

There are 5 vowels in the word 'ASSISSINATION'.

So, there are 6 ways of selecting a vowel.

Hence, required probability \[=\frac{6}{13}\]

But given that, \[\frac{6}{2x+1}=\frac{6}{13}\]

\[2x+1=13\,\,\,\,\Rightarrow \,\,\,\,2x=12\]

\[x=6\]