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?

Answers

  1. 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
    Learn more about the probability here:
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