Questions: The spinner shown is spun. (Assume that the size of each sector is the same.) Find the probability of the events in parts (a) through (g). a. The number is a factor of 35. P(factor of 35) = 3/8 (Type an integer or a simplified fraction.) b. The number is a multiple of 3. P(multiple of 3) = (Type an integer or a simplified fraction.)

The spinner shown is spun. (Assume that the size of each sector is the same.) Find the probability of the events in parts (a) through (g). a. The number is a factor of 35. P(factor of 35) = 3/8 (Type an integer or a simplified fraction.) b. The number is a multiple of 3. P(multiple of 3) = (Type an integer or a simplified fraction.)
Transcript text: The spinner shown is spun. (Assume that the size of each sector is the same.) Find the probability of the events in parts (a) through (g). a. The number is a factor of 35. $\mathrm{P}($ factor of 35$)=\frac{3}{8}$ (Type an integer or a simplified fraction.) b. The number is a multiple of 3 . $P($ multiple of 3$)=$ $\square$ (Type an integer or a simplified fraction.)
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Solution

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Solution Steps

Step 1: Identify the total number of sectors

The spinner has 8 sectors, each with an equal probability of being landed on.

Step 2: Determine the factors of 35

The factors of 35 are 1, 5, and 7.

Step 3: Count the sectors that are factors of 35

The sectors that are factors of 35 are 1, 5, and 7. There are 3 such sectors.

Final Answer

The probability that the number is a factor of 35 is \(\frac{3}{8}\).

Step 1: Identify the multiples of 3 on the spinner

The multiples of 3 on the spinner are 3 and 6.

Step 2: Count the sectors that are multiples of 3

The sectors that are multiples of 3 are 3 and 6. There are 2 such sectors.

Final Answer

The probability that the number is a multiple of 3 is \(\frac{2}{8} = \frac{1}{4}\).

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