Question

A bag contains 20 balls, some red and some purple. Suppose a student, without looking, chooses a ball out of the bag, records the color and then places the ball back in the bag. The student has recorded 3 red balls and 2 purple balls so far. Using these results, predict the number of red balls in the bag.

Answer 1

12 red balls

Explanation:

The number of balls recorded so far:

• Red = 3

,

• Purple = 2

This means that the relative frequency of obtaining a red ball will be:

`\text{ Relative Frequency for Red Ball}=(3)/(3+2)=(3)/(5)`
`\text{ Relative Frequency for Red Ball}=(3)/(3+2)=(3)/(5)`

Since there are 20 balls in the bag:

`\begin{gathered} \text{ Expected Outcome}=\text{ Relative Frequency}*\text{ Total Number of Trials} \\ =(3)/(5)*20 \\ =3*4 \\ =12\text{ red balls} \end{gathered}`

The number of red balls in the bag will be most likely 12.