Question

Two letters are chosen at random from the word MATHEMATICS, with replacement. What is the probability that the first letter is a consonant and the second letter is a vowel?

Answer 1

We want to know the probability of choosing two letters at random, and the first letter is a consonant and the second one is a vowel. The word we are given is

MATHEMATICS

We see that it has 7 consonants and 4 vowels. We will denote by E to the event:

`E=\text{`

As the events: "Obtaining a consonant" and "Obtaining a vowel" are independent, we get:

`P(E)=(7)/(11)\cdot(4)/(10)=(28)/(110)=(14)/(55)=0.25\bar{45}`

This means that the probability that the first letter is a consonant and the second letter is a vowel is (approximately) 25.45%.