Question

example 1
each spinner is spun. find the probability.

• p(a and 1): $\frac{3}{4}$
• p(a and 4):
• p(a vowel and odd number):
• p(a vowel and 5):

these are independent events - it does not matter what i spin on the first spinner, the second spinner is not affected
multiple choice question
what is the probability of getting a 7 on the second spinner?
options (not fully clear but typical for such): 1 (other option)
answer

Explanation:

Step1: Define single spinner probabilities

First spinner (8 equal sections): $P(2)=\frac{1}{8}$, $P(4)=\frac{1}{8}$, $P(\text{odd})=\frac{4}{8}=\frac{1}{2}$, $P(\text{vowel})=\frac{2}{8}=\frac{1}{4}$ (vowels are A, U)
Second spinner (8 equal sections): $P(1)=\frac{1}{8}$, $P(4)=\frac{1}{8}$, $P(\text{odd})=\frac{4}{8}=\frac{1}{2}$, $P(5)=\frac{1}{8}$

Step2: Calculate P(2 and 1)

Multiply independent probabilities:
$P(2 \text{ and } 1) = P(2) \times P(1) = \frac{1}{8} \times \frac{1}{8} = \frac{1}{64}$

Step3: Calculate P(4 and 4)

Multiply independent probabilities:
$P(4 \text{ and } 4) = P(4) \times P(4) = \frac{1}{8} \times \frac{1}{8} = \frac{1}{64}$

Step4: Calculate P(vowel and odd number)

Multiply independent probabilities:
$P(\text{vowel and odd}) = P(\text{vowel}) \times P(\text{odd}) = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}$

Step5: Calculate P(vowel and 5)

Multiply independent probabilities:
$P(\text{vowel and } 5) = P(\text{vowel}) \times P(5) = \frac{1}{4} \times \frac{1}{8} = \frac{1}{32}$

Step6: Calculate P(7 on second spinner)

Direct probability for second spinner:
$P(7 \text{ on second spinner}) = \frac{1}{8}$

Answer:

• $P(2 \text{ and } 1)$: $\frac{1}{64}$
• $P(4 \text{ and } 4)$: $\frac{1}{64}$
• $P(\text{vowel and odd number})$: $\frac{1}{8}$
• $P(\text{vowel and } 5)$: $\frac{1}{32}$
• Probability of getting a 7 on the second spinner: $\frac{1}{8}$