To find the probability of picking a consonant from the sample space \( S = {a, b, c, d, e, f} \), we first identify the consonants and vowels in the set.
The vowels in this set are:
- \( a \)
- \( e \)
The consonants in this set are:
- \( b \)
- \( c \)
- \( d \)
- \( f \)
So, there are 4 consonants (b, c, d, f) and 2 vowels (a, e).
The total number of outcomes in the sample space \( S \) is 6.
The probability \( P \) of picking a consonant is given by:
\[ P(\text{consonant}) = \frac{\text{Number of consonants}}{\text{Total number of outcomes}} = \frac{4}{6} \]
To simplify \(\frac{4}{6}\):
\[ \frac{4}{6} = \frac{2}{3} \]
Thus, the probability of picking a consonant is:
\[ \frac{2}{3} \]
Therefore, the correct answer is:
Start Fraction 2 over 3 End Fraction