Answer :
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:
[tex]E=\text{"Getting as a first letter a consonant and second letter a vowel"}[/tex]As the events: "Obtaining a consonant" and "Obtaining a vowel" are independent, we get:
[tex]P(E)=\frac{7}{11}\cdot\frac{4}{10}=\frac{28}{110}=\frac{14}{55}=0.25\bar{45}[/tex]This means that the probability that the first letter is a consonant and the second letter is a vowel is (approximately) 25.45%.
