Question

Outcome White Grey BlackNumber of Spins 35 32 33Fill in the table below. Round your answers to the nearest thousandth.(a) From Ivanna's results compute the experimental probability of landing on white.(b) Assuming that the spinner is fair, compute the theoretical probability of landing on white.(c) Assuming that the spinner is fair, choose the statement below that is true:The larger the number of spins, the greater the likelihood that the experimentalprobability will be close to the theoretical probabilityThe smaller the number of spins, the greater the likelihood that the experimentalprobability will be close to the theoretical probabilityThe experimental probability will never be very close to the theoretical probability, nomatter the number of spins

Answer 1

Experimental Probability depends not on purely reasoning but on the results of an experiment.

Outcome

White 35

Grey 32

Black 33

Total = 100

a) The results from Ivanna on landing on white:

In 100 times landings on white: 35

In 200 times landings on white: 62

In 300 times landings on white: 93

b) The Theoretical Probability of Landing on White

Since there are three colors, but only once is in our event:

`P_(white)=(1)/(3)`

In 100 rounds that would yield something like 33.3 (1/3*100)

In 100 times 33.3 landings on white

In 200 times 66.67 landings on white

In 300 times 100 landings on white

C) Based on the fact that :

|35 (experimental) - 33.3 (theoretical)| =1.7

|62 (experimental) -66.7| (theoretical) = 4.7

|93 (exp) -100( theo)| =7

The smaller the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability