Question:
Find the probability of getting the following from the word PROBABILITY.
Answer:
solve for Probability of desired event P(event) as,
[tex]\sf P(_{event}) = \frac{FO}{TO} \\\\where,\\\\\text{\sf P = Probability of Desired Event}\\\\\text{\sf FO = Favored Outcome = depends on desired event}\\\\\text{\sf TO = Total Outcome = 11 (11 letters in word - PROBABILITY)}[/tex]
#1. P(B)
[tex]\sf P(B) = \frac{FO}{TO} \\\\where,\\\\\text{\sf P = Probability of getting a letter B}\\\\\text{\sf FO = Favored Outcome = 2 (2 letter B in PROBABILITY)}\\\\\text{\sf TO = Total Outcome = 11 (11 letters in word - PROBABILITY)}\\\\\sf P(B) = \frac{FO}{TO} \\\\\sf P(B) = \frac{2}{11}[/tex]
#2. P(D)
[tex]\sf P(D) = \frac{FO}{TO} \\\\where,\\\\\text{\sf P = Probability of getting a letter D}\\\\\text{\sf FO = Favored Outcome = 0 (No letter D in PROBABILITY)}\\\\\text{\sf TO = Total Outcome = 11 (11 letters in word - PROBABILITY)}\\\\\sf P(D) = \frac{FO}{TO} \\\\\sf P(D) = \frac{0}{11}\\\\\sf P(D) = 0[/tex]
#3. P(A)
[tex]\sf P(A) = \frac{FO}{TO} \\\\where,\\\\\text{\sf P = Probability of getting a letter A}\\\\\text{\sf FO = Favored Outcome = 1 (1 letter A in PROBABILITY)}\\\\\text{\sf TO = Total Outcome = 11 (11 letters in word - PROBABILITY)}\\\\\sf P(A) = \frac{FO}{TO} \\\\\sf P(A) = \frac{1}{11}[/tex]
#4. P(all the vowels) --> FO = 4 because there are 4 vowels O, A, I, I
[tex]\sf P(all \;the \;vowels) = \frac{FO}{TO} \\\\where,\\\\\text{\sf P = Probability of getting all the vowels}\\\\\text{\sf FO = Favored Outcome = 4 (4 vowels in PROBABILITY)}\\\\\text{\sf TO = Total Outcome = 11 (11 letters in word - PROBABILITY)}\\\\\sf P(all \;the \;vowels) = \frac{FO}{TO} \\\\\sf P(all \;the \;vowels) = \frac{4}{11}[/tex]
#5. P(all the consonants) --> FO = 7 because there are 7 consonants P, R, B, B, L, T, Y
[tex]\sf P(all \;the \;consonants) = \frac{FO}{TO} \\\\where,\\\\\text{\sf P = Probability of getting all the consonants}\\\\\text{\sf FO = Favored Outcome = 7 (7 consonants in PROBABILITY)}\\\\\text{\sf TO = Total Outcome = 11 (11 letters in word - PROBABILITY)}\\\\\sf P(all \;the \;consonants) = \frac{FO}{TO} \\\\\sf P(all \;the \;consonants) = \frac{7}{11}[/tex]
#No to copy paste solution
#No to plagiarism
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