Question

An urn contains 10 red balls, 6 green balls, 15 orange balls, and 14 blue balls. If one ball is randomly drawn from the urn, what are the odds against the ball being blue?State your answer as a ratio (two numbers separated by a colon), but do not put any spaces in your response.

Answer 1

Given:

Red balls =10

Green balls =6

Orange ball =15

Blue ball =14

Total number of balls = 10+6+15+14 = 45

The probability that the randomly drawn ball is blue,

`\begin{gathered} P(B)=\frac{\text{Number of blue balls}}{\text{Total balls}} \\ P(B)=(14)/(45) \end{gathered}`

The probability that the randomly drawn ball is not blue,

`\begin{gathered} P(\text{ not B)=1-P(B)} \\ =1-(14)/(45)=(31)/(45) \end{gathered}`

The odds against event is calculated as,

`\begin{gathered} \text{Odds against=}\frac{P(\text{ not B)}}{P(B)} \\ =((31)/(45))/((14)/(45)) \\ =(31)/(45)*(45)/(14) \\ =(31)/(14) \end{gathered}`

Answer: the odds against the ball being blue is 31 : 14.