Chapter 13.3, Problem 26E

To determine

To find: The odds of drawing 2 red marbles.

Answer to Problem 26E

The odds of drawing 2 red marbles is $\frac{1}{4}$ .

Explanation of Solution

The number of green marbles are $1$ .

The number of yellow marbles are $2$ .

The number of red marbles are $3$ .

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

  $P\left(s\right)=\frac{s}{s+f}$

The probability of selection 2 red marbles is calculated as,

  $\begin{array}{c}P\left(\text{s}\right)=\frac{C\left(3,2\right)}{C\left(6,2\right)}\\ =\frac{1}{5}\end{array}$

The probability of failure is calculated as,

  $\begin{array}{c}P\left(f\right)=1-P\left(s\right)\\ =1-\frac{1}{5}\\ =\frac{4}{5}\end{array}$

The odds of 2 red marbled is calculated as,

  $\begin{array}{c}\text{Odds}=\frac{P\left(s\right)}{P\left(f\right)}\\ =\frac{1/5}{4/5}\\ =\frac{1}{4}\end{array}$

Therefore, the odds of 2 red marblesis $\frac{1}{4}$ .