Question

If you are choosing one state at random, are you more likely to choose a state whose name begins with a consonant or a vowel? what is the probability of each?

1. thienan
The probability that,
1) a state name begins with a consonant = 21/26
2) a state name begins with a vowel = 5/26
For give question,
We need to find the probability that
1) a state name begins with a consonant
2) a state name begins with a vowel
We know that the English Alphabet has 26 letters (a to z).
So, n(S) = 26
Let event A: the state name begins with a consonant
And event B: the state name begins with a vowel
In 26 alphabets, there are 5 vowels (a, e, i, o, u).
So, n(B) = 5
And out of 26 alphabets there are 21 consonants.
So, n(A) = 21
Now we find the required probability.
Using the formula for probability, the probability that a state name begins with a consonant would be,
⇒ P(A) = n(A)/n(S)
⇒ P(A) = 21/26
Similarly, using the formula for probability, the probability that a state name begins with a vowel would be,
⇒ P(B) = n(B)/n(S)
⇒ P(B) = 5/26
Therefore, the probability that
1) a state name begins with a consonant = 21/26
2) a state name begins with a vowel = 5/26