Question

The sample space of an experiment is S={a, b, c, d, e, f} . What is the probability of picking a consonant? Write your answer in the simplest fraction form.(1 point)
Responses

26
Start Fraction 2 over 6 End Fraction

23
Start Fraction 2 over 3 End Fraction

13
Start Fraction 1 over 3 End Fraction

32

Answer 1

The sample space is \( S = \{ a, b, c, d, e, f \} \).

To determine the probability of picking a consonant, we first need to identify the consonants in the sample space. The vowels are \( a \) and \( e \), and the consonants are \( b, c, d, \) and \( f \).

The consonants are:
- \( b \)
- \( c \)
- \( d \)
- \( f \)

This gives us a total of 4 consonants.

There are a total of 6 elements in the sample space (the total possible outcomes).

The probability \( P \) of picking a consonant can be calculated as follows:

\[
P(\text{consonant}) = \frac{\text{Number of consonants}}{\text{Total number of outcomes}} = \frac{4}{6}
\]

Now, we simplify \( \frac{4}{6} \):

\[
\frac{4}{6} = \frac{2}{3}
\]

Thus, the probability of picking a consonant is \( \frac{2}{3} \).

The correct answer is:
\[
\boxed{\frac{2}{3}}
\]