Question

A spinner with 10 equally sized slices has 4 yellow slices, 3 red slices, and 3 blue slices. Kaitlin spun the dial 1000 times and got the following results.Outcome YellowRed BlueNumber of Spins 421 299 280Answer the following. Round your answers to the nearest thousandths.(a)From Kaitlin's results, compute the experimental probability of landing on yellow or red.(b)Assuming that the spinner is fair, compute the theoretical probability of landing on yellow or red.(c)Assuming that the spinner is fair, choose the statement below that is true.The smaller the number of spins, the greater the likelihood that the experimental probabilitywill be close to the theoretical probability.The experimental probability will never be very close to the theoretical probability, no matterthe number of spins.The larger the number of spins, the greater the likelihood that the experimental probabilitywill be close to the theoretical probability.

Answer 1

The experimental probability of landing on yellow or red can be computed by adding the number of spins that landed on yellow with the number of spins that landed on red and dividing by the total number of spins. The theoretical probability of landing on yellow or red assuming the spinner is fair can be calculated by adding the probabilities of landing on yellow and red. The law of large numbers states that the larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.

Step-by-step explanation:

To compute the experimental probability of landing on yellow or red from Kaitlin's results, add the number of spins that landed on yellow with the number of spins that landed on red, and then divide this sum by the total number of spins. In this case, the experimental probability would be (421+299)/1000 = 0.72.

The theoretical probability of landing on yellow or red assuming the spinner is fair can be calculated by adding the probabilities of landing on yellow and red. In this case, the theoretical probability would be 4/10 + 3/10 = 0.7.

Based on the law of large numbers, the larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability. So, the statement that is true in this case is 'The larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.'

Answer 2

Given: A spinner with 10 equally sized slices has 4 yellow slices, 3 red slices, and 3 blue slices. Kaitlin spun the dial 1000 times and got the following results.

Outcome YellowRed Blue

Number of Spins 421 299 280

Required: Answer the following. Round your answers to the nearest thousandths.

(a)From Kaitlin's results, compute the experimental probability of landing on yellow or red.

(b)Assuming that the spinner is fair, compute the theoretical probability of landing on yellow or red.

(c)Assuming that the spinner is fair, choose the statement below that is true.

The smaller the number of spins, the greater the likelihood that the experimental probability

will be close to the theoretical probability.

The experimental probability will never be very close to the theoretical probability, no matter

the number of spins.

The larger the number of spins, the greater the likelihood that the experimental probability

will be close to the theoretical probability.

Step-by-step explanation:

(a)

`Experimental\text{ probability = }\frac{Number\text{ of trials in which the event occurs}}{Total\text{ number of trails}}`

The event E is landing on yellow or red.

Total number of trials = Number of times the dial is spun = 1000

Number of trials in which red or yellow occurs = 421+299 = 720

So the experimental probability of E is

`P(E)=(720)/(1000)=0.72`

(b)

`Theoretical\text{ Probability = }\frac{Favourable\text{ outcomes}}{Total\text{ Outcomes}}`

Total outcomes = Total slices in the dial = 10

Favourable outcomes = Yellow or red slices = 4+3 = 7

So theoretical probability is

`P(E)=(7)/(10)=0.7`

(c)

As the number of trials increases, the experimental probability and theoritical probability becomes closer and closer to each other.

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

Hence, statement 3 is true.

Final Answer:

(a) 0.72

(b) 0.7

(c) Statement 3