Answer:
a(n)=1.15[a(n-1)]
Step-by-step explanation:
we know that
Let
a0 -----> the length of the original copy
<em>The first copy is equal to</em>
a1=1.15(a0)
<em>The second copy is </em>
a2=1.15[1.15(a0)] or a2=1.15[a1]
<em>The third copy is</em>
a3=1.15{1.15[1.15(a0)]} or a3=1.15[a2]
therefore
A recursive formula will be
a(n)=1.15[a(n-1)]
There are 26 letters in the alphabet, 5 are vowels, therefore, the probability of choosing a vowel the first time is:
and the second time is:
Continuing with this reasoning, we get that the probabilities each time are:
Finally, the probability that you get all vowels is the product of the probabilities:
Writing the above result as a percentage we get:
Answer: