In a passage, there are 150 vowels out of which 32 are A's, 40 are E's and 30 are I's. What is the probability of next vowel being an O or an U?

The correct option is B 0.32
The five vowels of English alphabet are A, E, I, O and U.
Given, the number of vowels in the passage = 150
Number of A's, E's and I's = 32 + 40 + 30 = 102

We know, for an event E,
$P\left(E\right)=\frac{\text{Number of trials in which the event happened}}{\text{Total number of trials}}$

Hence,
P(next vowel being an A, E or I)$=\frac{102}{150}$

Also, we know, sum of probablities of all possible outcomes of an event is 1.

So, P(next vowel being an A, E or I) + P(next vowel not being an A, E or I) = 1
or, P(next vowel being an A, E or I) + P(next vowel being an O or an U) = 1
$⟹\text{P(next vowel being an O or an U)}=1-\frac{102}{150}=\frac{48}{150}=0.32$

[Alternatively,
Given, the number of vowels in the passage = 150
Number of A's, E's and I's = 32 + 40 + 30 = 102
Number of O's and U's = 150 - 102 = 48
P(next vowel being an O or an U)
$=\frac{48}{150}=0.32]$