Question

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Explanation:

First, define the sample spaces:

• Top spinner (letters): 4 equal sections: A, B, A, C. So total outcomes = 4. Vowels are A (2 sections).
• Bottom spinner (numbers): 6 equal sections: 1, 2, 2, 3, 4, 4. Total outcomes = 6.

Step1: Calculate P(A and 1)

Find P(A) and P(1), multiply (independent events).
$P(A) = \frac{2}{4} = \frac{1}{2}$, $P(1) = \frac{1}{6}$
$P(A \text{ and } 1) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}$

Step2: Calculate P(A and 4)

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

Step3: Calculate P(vowel and odd number)

Vowels are A (P=1/2), odd numbers are 1,3 (2 sections, $P(\text{odd}) = \frac{2}{6} = \frac{1}{3}$)
$P(\text{vowel and odd}) = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$

Step4: Calculate P(vowel and 5)

5 is not on the number spinner, so $P(5)=0$
$P(\text{vowel and } 5) = \frac{1}{2} \times 0 = 0$

Step5: Multiple-choice question

Probability of 1 on second spinner: $P(1) = \frac{1}{6}$

Answer:

• P(A and 1): $\frac{1}{12}$
• P(A and 4): $\frac{1}{6}$
• P(a vowel and odd number): $\frac{1}{6}$
• P(a vowel and 5): $0$
• Multiple-choice answer: $\frac{1}{6}$ (select the option for $\frac{1}{6}$)