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If a letter is chosen at random from the English alphabet, find the probability that the letter is chosen is 

(i) a vowel 

(ii) a consonant

1 Answer

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Best answer

(i) We know that,

Probability of occurrence of an event

   = \(\frac{Total\,no.of\,Desired\,outcomes}{Total\,no.of\,outcomes}\) 

Total possible outcomes are alphabets from a to z 

Desired outcomes are a, e, i, o, u 

Total no. of outcomes are 26 and desired outputs are 5 

Therefore, the probability of picking a vowel = \(\frac{5}{26}\)

Conclusion: Probability of choosing a vowel is  \(\frac{5}{26}\)

(ii) We know that, 

Probability of occurrence of an event 

   = \(\frac{Total\,no.of\,Desired\,outcomes}{Total\,no.of\,outcomes}\) 

Total possible outcomes are all alphabets from a to z

Desired outcomes are all alphabets except a, e, i, o, u 

Total no. of outcomes are 26 and desired outputs are 21 

Therefore, the probability of picking a consonant = \(\frac{21}{26}\)

Conclusion: Probability of choosing a consonant is  \(\frac{21}{26}\) 

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