QuestionA spinner has 3 yellow, 1 red, and 1 blue slice. After 1000 spins, Jane got 606 yellow, 181 red, 213 blue.
(a) Find the experimental probability of yellow or red. (b) Find the theoretical probability of yellow or red. (c) True statement about experimental vs theoretical probability with more spins?

Studdy Solution

STEP 1

Assumptions1. The spinner has5 equally sized slices3 yellow,1 red, and1 blue. . Jane spun the dial1000 times.
3. The results of the spins are606 yellow,181 red, and213 blue.
4. We are assuming that the spinner is fair, meaning each slice has an equal chance of being landed on.

STEP 2

(a) To compute the experimental probability of landing on yellow or red, we add the number of times Jane spun yellow or red and divide by the total number of spins.
$_{experimental}(Yellow\, or\, Red) = \frac{Number\, of\, Yellow\, spins + Number\, of\, Red\, spins}{Total\, number\, of\, spins}$

STEP 3

Now, plug in the given values for the number of yellow spins, red spins, and total spins to calculate the experimental probability.
$_{experimental}(Yellow\, or\, Red) = \frac{606 +181}{1000}$

STEP 4

Calculate the experimental probability of landing on yellow or red.
$_{experimental}(Yellow\, or\, Red) = \frac{787}{1000} =0.787$

STEP 5

(b) To compute the theoretical probability of landing on yellow or red, we add the number of yellow and red slices and divide by the total number of slices.
$_{theoretical}(Yellow\, or\, Red) = \frac{Number\, of\, Yellow\, slices + Number\, of\, Red\, slices}{Total\, number\, of\, slices}$

STEP 6

Now, plug in the given values for the number of yellow slices, red slices, and total slices to calculate the theoretical probability.
$_{theoretical}(Yellow\, or\, Red) = \frac{3 +1}{5}$

STEP 7

Calculate the theoretical probability of landing on yellow or red.
$_{theoretical}(Yellow\, or\, Red) = \frac{4}{5} =0.800$

STEP 8

(c) The statement that is true is "The larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability." This is based on the Law of Large Numbers, which states that as the number of trials increases, the experimental probability tends to get closer to the theoretical probability.
So, the answers are(a) The experimental probability of landing on yellow or red is0.787. (b) The theoretical probability of landing on yellow or red is0.800. (c) The larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.

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Studdy Solution

STEP 1

Assumptions1. The spinner has5 equally sized slices3 yellow,1 red, and1 blue. . Jane spun the dial1000 times.
3. The results of the spins are606 yellow,181 red, and213 blue.
4. We are assuming that the spinner is fair, meaning each slice has an equal chance of being landed on.

STEP 2

(a) To compute the experimental probability of landing on yellow or red, we add the number of times Jane spun yellow or red and divide by the total number of spins.
$_{experimental}(Yellow\, or\, Red) = \frac{Number\, of\, Yellow\, spins + Number\, of\, Red\, spins}{Total\, number\, of\, spins}$

STEP 3

Now, plug in the given values for the number of yellow spins, red spins, and total spins to calculate the experimental probability.
$_{experimental}(Yellow\, or\, Red) = \frac{606 +181}{1000}$

STEP 4

Calculate the experimental probability of landing on yellow or red.
$_{experimental}(Yellow\, or\, Red) = \frac{787}{1000} =0.787$

STEP 5

(b) To compute the theoretical probability of landing on yellow or red, we add the number of yellow and red slices and divide by the total number of slices.
$_{theoretical}(Yellow\, or\, Red) = \frac{Number\, of\, Yellow\, slices + Number\, of\, Red\, slices}{Total\, number\, of\, slices}$

STEP 6

Now, plug in the given values for the number of yellow slices, red slices, and total slices to calculate the theoretical probability.
$_{theoretical}(Yellow\, or\, Red) = \frac{3 +1}{5}$

STEP 7

Calculate the theoretical probability of landing on yellow or red.
$_{theoretical}(Yellow\, or\, Red) = \frac{4}{5} =0.800$

STEP 8

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Studdy Solution

STEP 1

Assumptions1. The spinner has5 equally sized slices3 yellow,1 red, and1 blue. . Jane spun the dial1000 times.3. The results of the spins are606 yellow,181 red, and213 blue.4. We are assuming that the spinner is fair, meaning each slice has an equal chance of being landed on.

STEP 2

STEP 3

Now, plug in the given values for the number of yellow spins, red spins, and total spins to calculate the experimental probability.experimental(Yellow or Red)=606+1811000_{experimental}(Yellow\, or\, Red) = \frac{606 +181}{1000}experimental​(YelloworRed)=1000606+181​

STEP 4

Calculate the experimental probability of landing on yellow or red.experimental(Yellow or Red)=7871000=0.787_{experimental}(Yellow\, or\, Red) = \frac{787}{1000} =0.787experimental​(YelloworRed)=1000787​=0.787

STEP 5

STEP 6

Now, plug in the given values for the number of yellow slices, red slices, and total slices to calculate the theoretical probability.theoretical(Yellow or Red)=3+15_{theoretical}(Yellow\, or\, Red) = \frac{3 +1}{5}theoretical​(YelloworRed)=53+1​

STEP 7

Calculate the theoretical probability of landing on yellow or red.theoretical(Yellow or Red)=45=0.800_{theoretical}(Yellow\, or\, Red) = \frac{4}{5} =0.800theoretical​(YelloworRed)=54​=0.800

STEP 8

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions1. The spinner has5 equally sized slices3 yellow,1 red, and1 blue. . Jane spun the dial1000 times.
3. The results of the spins are606 yellow,181 red, and213 blue.
4. We are assuming that the spinner is fair, meaning each slice has an equal chance of being landed on.

Now, plug in the given values for the number of yellow spins, red spins, and total spins to calculate the experimental probability.
$_{experimental}(Yellow\, or\, Red) = \frac{606 +181}{1000}$

Calculate the experimental probability of landing on yellow or red.
$_{experimental}(Yellow\, or\, Red) = \frac{787}{1000} =0.787$

Now, plug in the given values for the number of yellow slices, red slices, and total slices to calculate the theoretical probability.
$_{theoretical}(Yellow\, or\, Red) = \frac{3 +1}{5}$

Calculate the theoretical probability of landing on yellow or red.
$_{theoretical}(Yellow\, or\, Red) = \frac{4}{5} =0.800$