Question

A bag with 9 marbles is shown below. (2 marbles are blue, 3 are red, and 4 are yellow.) A marble is chosen from the bag at random. What are the oddsof choosing a blue marble?

Answer 1

`\text{odds}=\text{ 2:}7`

Step-by-step explanation

Step 1

find the probability:

Probabllity is the chance that a particular event will occur expressed on a linear scale from 0 to 1

The formula to calculate the probability of an event is as follows

`P=\frac{favorable\text{ outcomes}}{\text{total outcomes}}`

a) Let

`\begin{gathered} \text{favorable outcome= a blue marble = 2 ( there are 2 blue marbles)} \\ \text{total outcomes = 9 ( there are 9 marbles)} \end{gathered}`

now, replace

`\begin{gathered} P=\frac{favorable\text{ outcomes}}{\text{total outcomes}} \\ P=(2)/(9) \end{gathered}`

Step 2

find the odds

The odds are defined as the probability that the event will occur divided by the probability that the event will not occur.

`\text{odsds}=(P)/(1-P)=((2)/(9))/(1-(2)/(9))=((2)/(9))/((7)/(9))=(2\cdot9)/(7\cdot9)=(2)/(7)`

odds: 2:7

I hope this helps you