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?

Answers

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,

probabilitythat,consonant= 21/26vowel= 5/26probabilitythatconsonantvowelAlphabethas 26letters(a to z).consonantvowelalphabets, there are 5vowels(a, e, i, o, u).alphabetsthere are 21consonants.probability.probability, theprobabilitythat a state name begins with aconsonantwould be,probability, theprobabilitythat a state name begins with avowelwould be,probabilitythatconsonant= 21/26vowel= 5/26probabilityhere: