Given:
The letters of the word "history".
Required:
The probability that a selected letter,
a. Letter is a vowel.
b. The letter is a consonant.
Explanation:
The sample space is given as,
[tex]\begin{gathered} Sample\text{ space = }\lbrace\text{ h, i, s, t, o, r, y \textbraceright} \\ n(S)\text{ = 7} \end{gathered}[/tex]__(a)__
Assume A be the event the selected letter is a vowel.
The event A is given as,
[tex]\begin{gathered} A\text{ = \textbraceleft i, o \textbraceright} \\ n(A)\text{ = 2} \end{gathered}[/tex]The required probability is calculated as,
[tex]\begin{gathered} P(vowel)\text{ = }\frac{n(A)}{n(S)} \\ P(vowel)\text{ = }\frac{2}{7} \\ P(vowel)\text{ = 0.2857} \end{gathered}[/tex]__(b)__
Assume B be the event that a selected letter is a consonant.
The event B is given as,
[tex]\begin{gathered} B\text{ = \textbraceleft h, s, t, r, y \textbraceright} \\ n(B)\text{ = 5} \end{gathered}[/tex]The required probability is calculated as,
[tex]\begin{gathered} P(consonent)\text{ = }\frac{n(B)}{n(S)} \\ P(consonent)\text{ = }\frac{5}{7} \\ P(consonent)\text{ = 0.7143} \end{gathered}[/tex]Answer:
(a) Thus the probability that a selected letter is a vowel is 0.2857.
(b) Thus the probability that a selected letter is a consonant is 0.7143.