For how many pairs of vowels is the chance of occurrence of any one of the two more than 34% in the book?
4
5
6
7
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CAPF – 2023
$P(V) = \text{count}(V)/13$. So, we need $(\text{count}(V_i) + \text{count}(V_j))/13 > 0.34$, which simplifies to $\text{count}(V_i) + \text{count}(V_j) > 0.34 \times 13 = 4.42$.
The counts of the five vowels are {1, 3, 3, 3, 3}. Let’s examine the possible sums of counts for pairs of distinct vowels:
– Pair of counts (1, 3): Sum is $1+3=4$. $4 \ngtr 4.42$. There are 4 such pairs (the vowel with count 1 paired with each of the four vowels with count 3).
– Pair of counts (3, 3): Sum is $3+3=6$. $6 > 4.42$. There are 4 vowels with count 3. The number of pairs of distinct vowels chosen from these four is $\binom{4}{2} = \frac{4 \times 3}{2} = 6$.
Only the pairs of vowels with counts (3, 3) satisfy the condition. There are 6 such pairs. This matches option C. This inferred data also consistently works for Q26775.