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)=(4)/(7) \\ P(T)=(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)=(1)/(7) \end{gathered}`

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

`P(TIC)=(P(T\cap C))/(P(C))`
`\begin{gathered} P(TIC)=((1)/(7))/((4)/(7)) \\ P(TIC)=(1)/(7)/(4)/(7) \\ P(TIC)=(1)/(7)*(7)/(4) \\ P(TIC)=(1)/(4) \end{gathered}`

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