Question

A letter is chosen at random from the word COMPUTE. Find the probability of the letter being T given it is a consonant.1/21/31/41/7

Answer 1

Given: The word COMPUTE

To Determine: The probability of the letter being T given it is a consonant

Solution

Let us write the consonants in the word COMPUTE

$Consonants(C)=\lbrace C,M,P,T\rbrace$$Letter(T)=\lbrace T\rbrace$$Given(Word)(W)=\lbrace C,O,M,P,U,T,E\rbrace$

Let us find the cardinality of each

$\begin{gathered} n(C)=4 \\ n(T)=1 \\ n(W)=7 \end{gathered}$

Let us find the probaility of chosen letter T and consonants

$\begin{gathered} P(C)=\frac{4}{7} \\ P(T)=\frac{1}{7} \end{gathered}$

Let us find the probability of T and consonants

$\begin{gathered} T\cap C=\lbrace T\rbrace \\ n(T\cap C)=1 \\ P(T\cap C)=\frac{1}{7} \end{gathered}$

So, The probability of the letter being T given it is a consonant would be

$P(TIC)=\frac{P(T\cap C)}{P(C)}$$\begin{gathered} P(TIC)=\frac{\frac{1}{7}}{\frac{4}{7}} \\ P(TIC)=\frac{1}{7}\div\frac{4}{7} \\ P(TIC)=\frac{1}{7}\times\frac{7}{4} \\ P(TIC)=\frac{1}{4} \end{gathered}$

Hence, the probability of the letter being T given it is a consonant is 1/4