Question

if the wheel is spun and each section is equally likely to stop under the pointer, determine the probability that the pointer lands on an odd number, given that the color is red or purple. note that the purple sectors are the sectors numbered 2, 4, 9, 11, and 12; the gold sectors are numbered 3 and 10; and the red sectors are numbered 5, 6, and 7.

what is the probability?

(type an integer or a simplified fraction.)

Explanation:

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<reasoning>

Identify the given condition and sample space

The condition is that the landed sector is red or purple.
The purple sectors are: \(2, 4, 9, 11, 12\)
The red sectors are: \(5, 6, 7\)
The reduced sample space \(A\) (red or purple) is:
\[
A = \{2, 4, 5, 6, 7, 9, 11, 12\}
\]
The total number of outcomes in this reduced sample space is:
\[
n(A) = 8
\]

Identify the favorable outcomes

We need the number to be odd, given it is in the reduced sample space \(A\).
The odd numbers in \(A\) are:
\[
B = \{5, 7, 9, 11\}
\]
The number of favorable outcomes is:
\[
n(B) = 4
\]

Calculate the conditional probability

The probability is the ratio of favorable outcomes to the total outcomes in the reduced sample space:
\[
P = \frac{n(B)}{n(A)} = \frac{4}{8} = \frac{1}{2}
\]
</reasoning>

<answer>
What is the probability?

<blank>\(\frac{1}{2}\)</blank> (Type an integer or a simplified fraction.)
</answer>

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Answer:

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<reasoning>

Identify the given condition and sample space

The condition is that the landed sector is red or purple.
The purple sectors are: \(2, 4, 9, 11, 12\)
The red sectors are: \(5, 6, 7\)
The reduced sample space \(A\) (red or purple) is:
\[
A = \{2, 4, 5, 6, 7, 9, 11, 12\}
\]
The total number of outcomes in this reduced sample space is:
\[
n(A) = 8
\]

Identify the favorable outcomes

We need the number to be odd, given it is in the reduced sample space \(A\).
The odd numbers in \(A\) are:
\[
B = \{5, 7, 9, 11\}
\]
The number of favorable outcomes is:
\[
n(B) = 4
\]

Calculate the conditional probability

The probability is the ratio of favorable outcomes to the total outcomes in the reduced sample space:
\[
P = \frac{n(B)}{n(A)} = \frac{4}{8} = \frac{1}{2}
\]
</reasoning>

<answer>
What is the probability?

<blank>\(\frac{1}{2}\)</blank> (Type an integer or a simplified fraction.)
</answer>

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