Each of the letters of the word ‘AUTHORIZES’ is written on identical circular discs

Probability (10)

Each of the letters of the word ‘AUTHORIZES’ is written on identical circular discs and put in a bag. They are well shuffled. If a disc is drawn at random from the bag, what is the probability that the letter is:

1. a vowel
2. one of the first 9 letters of the English alphabet which appears in the given word
3. one of the last 9 letters of the English alphabet which appears in the given word?

Answer

I. {𝐴, 𝑈, 𝑇, 𝐻, 𝑂, 𝑂, 𝐼, 𝑍, 𝐸, 𝑆} 10 letter

Vowels are {𝐴, 𝐸, 𝐼, 𝑂, 𝑈} 5 letters

∴ prob. is = 5/10 = 1/2

ii.  {𝐴, 𝐸, 𝐻, 𝐼}

∴ prob. is = 4/10 = 2/5

iii. {R, 𝑆, 𝑇, 𝑈, 𝑍}

∴ prob. is =5/10 = 12