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Question

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?

A
0.15
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B
0.32
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C
0.68
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D
0.85
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Solution

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(E)=Number of trials in which the event happenedTotal number of trials

Hence,
P(next vowel being an A, E or I)=102150

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
P(next vowel being an O or an U)=1102150=48150=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)
=48150=0.32 ]

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