Chapter 6, Problem 22CT

To determine

To find the probability of choosing a red marble and the odds in favor of choosing a green marble.

Answer to Problem 22CT

The probability of getting a red marble is $\frac{2}{15}$ .

The odds in favor of getting a green marble is $\frac{1}{2}$ .

Explanation of Solution

Given information:

A bag contains $8$ blue marbles, $6$ red marbles, $15$ green marbles and $16$ orange marbles

Formula used:

The formulas used are:

  $\begin{array}{l}\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}\\ \text{Odds in Favor}=\frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}}\end{array}$

Calculation :

The total number of possible outcomes are $45$ and the number of favorable outcomes are $6$

The probability of getting a red marble can be calculated by:

  $\begin{array}{l}\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}\\ \text{Probability}=\frac{6}{45}\\ \text{Probability}=\frac{2}{15}\left[\text{Simplify}\right]\end{array}$

Hence, the probability of getting a red marble is $\frac{2}{15}$ .

The total number of favorable outcomes are $15$ and the number of unfavorable outcomes are $30$

The odds in favor of getting a green marble can be calculated by:

  $\begin{array}{l}\text{Odds in Favor}=\frac{\text{Number of favorable outcomes}}{\text{Number of unfavorable outcomes}}\\ \text{Odds in Favor}=\frac{15}{30}\\ \text{Odds in Favor}=\frac{1}{2}\left[\text{Simplify}\right]\end{array}$

Hence, the odds in favor of getting a green marble is $\frac{1}{2}$ .