Question

A spinner with 5 equally sized slices has 2 yellow slices, 2 red slices, and 1 blue slice. Yolanda spun the dial 40 times and got the following results. Answer the following. Round your answer to the nearest thousandth

Answer 1

Given: A spinner with 5 equally sized slices has 2 yellow slices, 2 red slices, and 1 blue slice.

Yolanda spun the dial 40 times and got Yellow 13 times, Red 13 times and Blue 14 times.

Required:

(a) Experimental probability of landing on Blue or Red

(b) Theoretical probability of landing on Blue or Red

(c) What happens when number of spins increases.

Explanation:

(a) Experimental probability =

`Experimental\text{ Probability = }\frac{Number\text{ of trials in which the event occurs}}{total\text{ number of trials}}`

Here, the event is landing on blue or red.

Number of trials in which Blue or Red occurs is 14+13=27

Total number of trials is 40.

So experimental probability is

`(27)/(40)=0.675`

Hence, experimental probability is 0.675.

(b) Theoretical probability is

`Theoretical\text{ Probability = }\frac{Favorable\text{ Outcome}}{total\text{ outcome}}`

Here, favorable outcomes for red and blue = 2+1 = 3.

And total possible outcomes = 5

So theoretical probability is

`(3)/(5)=0.6`

Hence, theoretical probability is 0.6.

(c) Now, as the number of spins will increase, number of trials will increase and experimental probability will become more and more precise. Hence, it will come closer to theoretical property. So both probabilities will become closer and closer though they might not be equal.

Final Answer:

(a) 0.675

(b) 0.600

(c) Option 1