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?

Respuesta :

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,

[tex]\begin{gathered} P=\frac{Number\text{ of letter P}}{\text{Total letters}} \\ P=\frac{2}{11} \end{gathered}[/tex]

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

[tex]\begin{gathered} P^{\prime}=1-\frac{2}{11} \\ P^{\prime}=\frac{9}{11} \end{gathered}[/tex]

The odd against event is calculated as,

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

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