Question

All eleven letters from the word MISSISSIPPI are written on individual slips of paper and placed in a hat. If you reach into the hat and randomly choose one slip of paper, what are the odds against the paper having the letter P written on it?

Answer 1

Given:

There are 11 letters in the word 'MISSISSIPPI'

The number of P's are 2.

The probability that the randomly chosen slip of paper have the letter P written on it is,

`\begin{gathered} P=\frac{Number\text{ of letter P}}{\text{Total letters}} \\ P=(2)/(11) \end{gathered}`

The probability that the randomly chosen slip of paperdoes not have the letter P written on it is,

`\begin{gathered} P^(\prime)=1-(2)/(11) \\ P^(\prime)=(9)/(11) \end{gathered}`

The odd against event is calculated as,

`\begin{gathered} Odd\text{ against=}\frac{P(not\text{ E)}}{P(E)} \\ Odd\text{ against}=(P^(\prime))/(P)=((9)/(11))/((2)/(11))=(9)/(2) \end{gathered}`

Answer: The odds against the paper having the letter P written on it is 9/2 (9:2)