Chapter 13.3, Problem 39E

(a)

To determine

To find: The probability of guessing the correct combination.

Answer to Problem 39E

The probability of guessing the correct combination is $\frac{13}{27}$

Explanation of Solution

The probability of the successful outcome of an event is given by,

  $P\left(s\right)=\frac{s}{s+f}$

The probability of failure is given by,

  $P\left(f\right)=1-P\left(s\right)$

The probability of guessing the correct combination is calculated as,

  $\begin{array}{c}P\left(s\right)=\frac{C\left(1,1\right)}{C\left(10,3\right)}\\ =\frac{1}{120}\end{array}$

Therefore, the probability of guessing the correct combination is $\frac{1}{120}$

(b)

To determine

To find: The odds of guessing the correct combination.

Answer to Problem 39E

The odds of guessing the correct combination is $\frac{999}{1000}$

Explanation of Solution

The probability of the successful outcome of an event is given by,

  $P\left(s\right)=\frac{s}{s+f}$

The probability of failure is given by,

  $P\left(f\right)=1-P\left(s\right)$

The probability of guessing the correct combination is calculated as,

  $\begin{array}{c}P\left(s\right)=\frac{1}{{10}^3}\\ =\frac{1}{1000}\end{array}$

The odds of an event is given by,

  $\begin{array}{c}\text{Odds}=\frac{P\left(s\right)}{P\left(f\right)}\\ =\frac{P\left(s\right)}{1-P\left(s\right)}\\ =\frac{\frac{1}{1000}}{1-\frac{1}{1000}}\\ =\frac{999}{1000}\end{array}$

Therefore, the odds of guessing the correct combination is $\frac{999}{1000}$