Question

You can earn 1 coinEach group of students receives a bag that has 9 red cubes, 5 green cubes, and 11 bluecubes. If each group makes 1000 pulls and replaces the cube after each pull, how manytimes would you expect them to draw a blue cube?

Answer 1

The bag has a total of 25 cubes, of which, 9 are red, 5 are green and 11 are blue.

The groups of kids will pull one cube of the bag, register its color and then put the cube back in the bag, this will be repeated 1000 times.

To determine how many times it is expected to draw a blue cube of the bag, the first step is to determine the probability that, when a kid takes a cube from the bag, the said cube will be blue.

The probability of the cube being blue can be calculated as the quotient between the number of blue cubes in the bag and the total number of cubes in the bag:

`\begin{gathered} P(blue)=\frac{nº\text{blue cubes}}{nº\text{cubes}} \\ P(blue)=(11)/(25) \\ P(blue)=0.44 \end{gathered}`

→ This means that the probability of pulling a blue cube when a kid takes a cube from the bag is 0.44.

Now, to calculate the expected number of times a blue cube will be pulled from the bag you have to multiply the probability of the cube being blue by the number of times a cube was pulled from the bag, as follows: