Braille:-

In Braille, each character consists of a pattern of raised dots. There are six positions in a character, each of which can be either flat or raised. This gives a total of 26 or 64 possible letters that can be described by a single Braille character. For standard English there are more than 64 symbols to be described; a to z in both lower and upper case, 0 to 9, and standard punctuation (space, comma, etc.). Thus, some symbols require more than one Braille character. Suppose 8 percent of letters are capitalized and 12 percent of letters are digits.

(a) In Grade 1 Braille, lowercase letters and standard punctuation all require a single character. There is also a special character that indicates that the following character will describe a capital letter. Similarly, there is a special character to indicate that the following character will describe a digit. What is the expected number of Braille characters used to describe a standard English letter?

(b) In Grade 2 Braille, in addition to the characters denoting capitals and digits, there are single characters that are used to denote common groups of letters (for example, the, and, ing). Suppose that each group of letters is three long and that 20 percent of standard English text comes from one of the common letter groups used in Grade 2 Braille. What is the expected number of Braille characters used to describe a standard English letter?