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Complement of an Event

The letters o...

Question

The letters of the word AUDIT are rearranged.

What is the probability of (i) A new word starting with a vowel (ii) A new word starting with a consonant?

Are one and two complementary events?

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Solution

(i) Since there are 3 vowels out of 5 letters, the probability = $\frac{3}{5}$ = 0.6.

(ii) Since there are 2 vowels out of 5 letters, the probability = $\frac{2}{5}$ = 0.4.

These two are complementary events because if a word starts with a vowel, then it cannot begin with a consonant and vice versa.

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