Question

A bag of 25 marble, five a red, seven are blue, ten are green, and three are yellow. the results of a marvel being randomly selected and replace by 50 times are shown in the table. for which color is the experimental probability closest to the theoretical probability of being selected. Explain.

Answer 1

The experimental probability closest to the theoretical probability is for the green marble.

Number of red marbles selected = 5

Number of blue marbles selected = 7

Number of green marbles selected = 10

Number of yellow marbles selected = 3

Total number of selections: 50

Theoretical Probabilities:

`P_(theoretical)(Red) = (5)/(25)=(1)/(5) = 0.2`

`P_(theoretical)(Blue) = (7)/(25) = 0.28`

`P_(theoretical)(Green) = (10)/(25)=(2)/(5) = 0.4`

`P_(theoretical)(Yellow) = (3)/(25) = 0.12`

Experimental Probabilities:

To calculate the experimental probabilities, we need the actual counts of each color after 50 randomly selected marbles. Let's say, for example, that the counts are as follows:

Number of red marbles selected = 12

Number of blue marbles selected = 18

Number of green marbles selected = 15

Number of yellow marbles selected = 5

`P_(experimental)(Red) = (12)/(50)=0.24`

`P_(experimental)(Blue) = (18)/(50)=0.36`

`P_(experimental)(Green) = (15)/(50)=0.3`

`P_(experimental)(Yellow) = (5)/(50)=0.1`

Comparing the experimental and theoretical probabilities, we can see that the experimental probability closest to the theoretical probability is for the green marble.