Answer:
a) 0.125
b) 0.041[tex]\bar 6[/tex]
c) 0.458[tex]\bar 3[/tex]
d) 0.541[tex]\bar 6[/tex]
e) 0.0763[tex]\bar 8[/tex]
Step-by-step explanation:
The number of letters in the name THE UNITED STATES OF AMERICA = 24
The probability of a particular outcome occurring = (The number of required outcome)/(The number of possible outcome)
The number of possible letters the computer can pick = 24, therefore the number of possible outcome = 24
a) The number of As in the name = 3 As
The number of required outcome = 3
Therefore, the probability the probability that the letter is an A = 3/24 = 1/8 = 0.125
b) The number of Ms in the name = 1 M
Which gives the number of required outcome = 1
Therefore, the probability the probability that the letter is a M = 1/24 = 1/24 = 0.041[tex]\bar 6[/tex]
c) The vowels in the name are E, U, I, E, A, E, O, A, E, I, A which are 11 in number
Which gives the number of required outcome = 11
Therefore, the probability the probability that the computer picks a vowel = 11/24 = 0.458[tex]\bar 3[/tex]
d) The number of consonants = The number of letters in the name - The number of vowels
∴ The number of consonants = 24 - 11 = 13 consonants
Which gives the number of required outcome = 13
Therefore, the probability the probability that the computer picks a consonant = 13/24 = 0.541[tex]\bar 6[/tex]
e) The number of letter Ts in the name are 4 Ts
The probability that the computer picks a letter T = 4/24 = 1/6
The probability that the computer picks a vowel and a letter T is given by the product of the two probabilities as follows
P(Vowel and Letter T) = P(Vowel) × P(Letter T) = 11/24 × 1/6 = 11/144 = 0.0763[tex]\bar 8[/tex].
