The letters of the alphabet are written on 26 cards. Two cards are chosen at random. Find the probability that at least one of them is a vowel ?

Engineering

Mathematics

Basic Definitions Related to Probability

Question

$\frac{23}{65}$

$\frac{13}{24}$

$\frac{5}{65}$

$\frac{1}{23}$

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The complement of A' at least one of them is vowels is neither of them is a vowel.

There are 5 vowels and 21 are consonants P (The first card chosen is not a vowel)

= \frac{21}{26}

P (The second card chosen is also not a vowel)

= \frac{20}{25}

P (Neither of them is a vowel)

= \frac{21}{26} \times \frac{20}{25} = \frac{42}{65}

P (At least one of them is a vowel)

= 1 - \frac{42}{65} = \frac{23}{65}