Question

multiple - choice question
what is \\(\frac{1}{3}\\) written as a percentage?
options (partially visible):...

example 1
each spinner is spun. find the probability.
\\(p(a\text{ and }t)=\frac{2}{4}\cdot\frac{2}{6}=\frac{4}{24}=\frac{1}{6}\\)

• \\(p(a\text{ and }a)\\)
• \\(p(\text{even and odd number})\\)
• \\(p(3\text{ (vowel) and }s)\\)

two are independent events - it does not matter what i spin on the first spinner.

Explanation:

First, let's address the multiple-choice question at the bottom, then solve the spinner probability problems:

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Multiple-Choice Question

Step1: Convert fraction to decimal

$\frac{1}{21} \approx 0.0476$

Step2: Convert decimal to percentage

$0.0476 \times 100 = 4.76\% \approx 5\%$

First, define the sample spaces:

• Top spinner (4 sections): $\{A, E, A, O\}$ (all are vowels; 2 out of 4 are "A")
• Bottom spinner (6 sections): $\{1, 4, 4, 3, 2, 5\}$

Step1: Solve P(A and 1)

Calculate individual probabilities, multiply.
$P(A) = \frac{2}{4} = \frac{1}{2}$, $P(1) = \frac{1}{6}$
$P(A \text{ and } 1) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}$

Step2: Solve P(A and 4)

Calculate individual probabilities, multiply.
$P(A) = \frac{2}{4} = \frac{1}{2}$, $P(4) = \frac{2}{6} = \frac{1}{3}$
$P(A \text{ and } 4) = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$

Step3: Solve P(vowel and odd number)

All top spinner sections are vowels, so $P(\text{vowel})=1$. Odd numbers on bottom spinner: $\{1,3,5\}$, so $P(\text{odd})=\frac{3}{6}=\frac{1}{2}$
$P(\text{vowel and odd}) = 1 \times \frac{1}{2} = \frac{1}{2}$

Step4: Solve P(vowel and 5)

All top spinner sections are vowels, so $P(\text{vowel})=1$. $P(5)=\frac{1}{6}$
$P(\text{vowel and } 5) = 1 \times \frac{1}{6} = \frac{1}{6}$

Answer:

B. 5%

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Spinner Probability Problems