b Redo your calculations of the expected value of the left spinner.
A
a The class should choose the right spinner.
B
b The class should choose the left spinner.
Practice makes perfect
a To determine which spinner the class should choose, we have to think about the expected value of each spinner. The expected value of a region in the spinner is the product of that region's value and the probability that the region is spun. The probability is the central angle of that region divided by 360^(∘).
Finally, we will multiply the region's payout with its corresponding probability.
l|l
Left spinner & Right spinner
20: 1/4(20)=5 & 10: 1/2(10)=5 [0.8em]
& 5: 1/2(5)=2.5
Since there is only one region in the left spinner that pays off, the expected value is 5. To obtain the expected value of the right spinner, we have to add the expected value of both regions to get the total expected value per spin.
5+2.5=7.5
As we can see, the expected value from the right spinner is higher. Therefore, the class should choose this spinner.
b If the spot labeled 20 was changed to 100, the expected value of the left spinner will change.
20: 1/4(100)=25
Now,the expected value from the left spinner is 25. Therefore, the left spinner should be chosen.
