Question

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?

• A. $\frac{23}{65}$
• B. $\frac{13}{24}$
• C. $\frac{5}{65}$
• D. $\frac{1}{23}$

Answer 1

The correct option is A $\frac{23}{65}$

The complement of $A^{\prime }$ 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) $=$ $1-\frac{42}{65}=\frac{23}{65}$