Questions: Use the spinner shown. It is equally probable that the pointer will land on any one of the eight regions. If the pointer lands on a borderline, spin again. If the pointer is spun three times, find the probability that it will land on green and then purple and then blue. Find the probability that the spinner will land on green and then purple and then blue. (Type an integer or a simplified fraction.)

Use the spinner shown. It is equally probable that the pointer will land on any one of the eight regions. If the pointer lands on a borderline, spin again. If the pointer is spun three times, find the probability that it will land on green and then purple and then blue. Find the probability that the spinner will land on green and then purple and then blue. (Type an integer or a simplified fraction.)
Transcript text: Use the spinner shown. It is equally probable that the pointer will land on any one of the eight regions. If the pointer lands on a borderline, spin again. If the pointer is spun three times, find the probability that it will land on green and then purple and then blue Find the probability that the spinner will land on green and then purple and then blue. $\square$ (Type an integer or a simplified fraction.)
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Solution

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Solution Steps

Step 1: Find the probability of landing on green.

There are 2 green sections out of 8 total sections. The probability of landing on green is 2/8 = 1/4.

Step 2: Find the probability of landing on purple.

There is 1 purple section out of 8 total sections. The probability of landing on purple is 1/8.

Step 3: Find the probability of landing on blue.

There are 2 blue sections out of 8 total sections. The probability of landing on blue is 2/8 = 1/4.

Step 4: Find the probability of all three events occurring.

Since the spins are independent events, we multiply the probabilities: (1/4) * (1/8) * (1/4) = 1/128

Final Answer:

1/128

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