Question

You put the letters SCHOOL into a bag. What is the probability that you pull a Lout on your first pick, set it aside, and then pull a vowel? answer choices: 1/18 1/15 3/11 1/10

Answer 1

Let's begin by identifying key information given to us:

Total number of letters = 6

Number of letter "L" = 1

Number of vowels = 2

The probability that you pull an "L" out on your first pick is:

$\begin{gathered} P(L)=\frac{no\mathrm{}of\mathrm{}LetterL}{Total.no} \\ P(L)=\frac{1}{6} \end{gathered}$

The probability that you pull a vowel afterwards is:

$\begin{gathered} P(vowel)=\frac{no\mathrm{}of\mathrm{}vowels}{Total\mathrm{}letters.left} \\ P(vowel)=\frac{2}{6-1}=\frac{2}{5} \\ P(vowel)=\frac{2}{5} \end{gathered}$

The total probability of this event is given by the product of P(L) & P(vowel):

$\begin{gathered} P(Total)=P(L)\cdot P(vowel) \\ P(Total)=\frac{1}{6}\cdot\frac{2}{5}=\frac{1\cdot2}{6\cdot5} \\ P(Total)=\frac{2}{30}=\frac{1}{15} \\ P(Total)=\frac{1}{15} \end{gathered}$

Hence, the probability of this event is 1/15