Question

1. if you spin the blue spinner and yellow spinner, what is the probability that you will land on a section marked \3\ on both spinners? 1/50 12) if you spin all four spinners, what is the probability that all will land on a number that is at least 2?

Explanation:

Question 11

Step1: Determine blue spinner sections

The blue spinner has 10 equal sections (numbers 0 - 9). The number of sections marked "3" is 1. So, the probability of landing on "3" for the blue spinner, \( P(\text{blue}=3) = \frac{1}{10} \).

Step2: Determine yellow spinner sections

The yellow spinner has 5 equal sections (numbers 1 - 5). The number of sections marked "3" is 1. So, the probability of landing on "3" for the yellow spinner, \( P(\text{yellow}=3) = \frac{1}{5} \).

Step3: Calculate combined probability

Since the spins are independent events, the probability of both events happening is the product of their individual probabilities. So, \( P(\text{both}=3) = P(\text{blue}=3) \times P(\text{yellow}=3) = \frac{1}{10} \times \frac{1}{5} = \frac{1}{50} \).

Step1: Analyze each spinner

• Blue spinner (10 sections: 0 - 9): Numbers at least 2 are 2 - 9, so 8 sections. Probability \( P(\text{blue} \geq 2) = \frac{8}{10} = \frac{4}{5} \).
• Yellow spinner (5 sections: 1 - 5): Numbers at least 2 are 2 - 5, so 4 sections. Probability \( P(\text{yellow} \geq 2) = \frac{4}{5} \).
• Red spinner (6 sections: 1 - 6): Numbers at least 2 are 2 - 6, so 5 sections. Probability \( P(\text{red} \geq 2) = \frac{5}{6} \).
• Green spinner (8 sections: 1 - 8): Numbers at least 2 are 2 - 8, so 7 sections. Probability \( P(\text{green} \geq 2) = \frac{7}{8} \).

Step2: Calculate combined probability

Since the spins are independent, the probability that all four spinners land on a number at least 2 is the product of their individual probabilities:
\[

$$\begin{align*} P(\text{all} \geq 2) &= \frac{4}{5} \times \frac{4}{5} \times \frac{5}{6} \times \frac{7}{8}\\ &= \frac{4 \times 4 \times 5 \times 7}{5 \times 5 \times 6 \times 8}\\ &= \frac{4 \times 4 \times 7}{5 \times 6 \times 8}\\ &= \frac{112}{240}\\ &= \frac{7}{15} \end{align*}$$

\]

Answer:

\(\frac{1}{50}\)

Question 12