Question

if a letter is chosen at random from the 10 letters of the word statistics wat is probability that it is a vowel?

Answer 1

Given, $n=10$ , Total number of vowels in word ' STATISTICS'=3

Let p denote the probability of vowel $p=\dfrac{5}{26}=0.192$

Then $q=1-p=1-0.192=0.8076$

Probability that selected letter is vowel-

$=^{10}C_3 p^3q^{10-3}\\=^{10}C_3(0.192)^3(0.8076)^7\\=120\times0.00707\times 0.224\\=0.19$