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A spinner has four equally sized sectors that are numbered 1,2,6 and 6 . the spinner is spun twice and the product of the outcomes is found . a fair decision is to be made about which one of four flowers will be planted. The flower options are peonies, roses, asters and petunias

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Answer: To find the probability of getting a certain product from spinning the spinner twice, we need to calculate all the possible products and their associated probabilities.

The possible outcomes for each spin and their respective probabilities are as follows:

Spinner outcomes: {1, 2, 6, 6}

Probabilities: {1/4, 1/4, 1/4, 1/4}

Now, let's find all the possible products of two spins and their probabilities:

Product of two 1's: 1 * 1 = 1

Probability: (1/4) * (1/4) = 1/16

Product of 1 and 2: 1 * 2 = 2

Probability: (1/4) * (1/4) = 1/16

Product of 1 and 6: 1 * 6 = 6

Probability: (1/4) * (1/4) = 1/16

Product of two 2's: 2 * 2 = 4

Probability: (1/4) * (1/4) = 1/16

Product of 2 and 6: 2 * 6 = 12

Probability: (1/4) * (1/4) = 1/16

Product of two 6's: 6 * 6 = 36

Probability: (1/4) * (1/4) = 1/16

Now, we can determine the probability of each product and choose the flower to plant based on a fair decision.

Probability of product 1: 1/16

Probability of product 2: 1/16

Probability of product 6: 1/16

Probability of product 4: 1/16

Probability of product 12: 1/16

Probability of product 36: 1/16

Since all the products have the same probability of 1/16, it is a fair decision to choose any of the flowers for planting. Each flower has an equal probability of being selected based on the product of the outcomes from spinning the spinner twice. Therefore, it's up to personal preference or other criteria to decide which flower to plant.

User Prashant Gami
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