Question

a spinner contains four equally shaded areas, as shown below.
spinner image: orange, blue, blue, green (four equal sections)
louise spins the spinner twice. which probabilities are correct? check all that apply.

• $p(\text{both green}) = \frac{1}{16}$
• $p(\text{both blue}) = \frac{1}{4}$
• $p(\text{first green and then blue}) = \frac{1}{6}$
• $p(\text{first orange and then blue}) = \frac{1}{8}$
• $p(\text{first orange and then green}) = \frac{1}{4}$

Explanation:

Step1: Determine single spin probabilities

The spinner has 4 equal areas: orange (1), blue (2), green (1). So \( P(\text{orange}) = \frac{1}{4} \), \( P(\text{blue}) = \frac{2}{4}=\frac{1}{2} \), \( P(\text{green}) = \frac{1}{4} \). Spins are independent, so \( P(A \text{ and } B) = P(A) \times P(B) \).

Step2: Check \( P(\text{both green}) \)

\( P(\text{green}) \times P(\text{green}) = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} \). Correct.

Step3: Check \( P(\text{both blue}) \)

\( P(\text{blue}) \times P(\text{blue}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \). Correct.

Step4: Check \( P(\text{first green and then blue}) \)

\( P(\text{green}) \times P(\text{blue}) = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}
eq \frac{1}{6} \). Incorrect.

Step5: Check \( P(\text{first orange and then blue}) \)

\( P(\text{orange}) \times P(\text{blue}) = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} \). Correct.

Step6: Check \( P(\text{first orange and then green}) \)

\( P(\text{orange}) \times P(\text{green}) = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16}
eq \frac{1}{4} \). Incorrect.

Answer:

• \( P(\text{both green}) = \frac{1}{16} \) (Correct)
• \( P(\text{both blue}) = \frac{1}{4} \) (Correct)
• \( P(\text{first orange and then blue}) = \frac{1}{8} \) (Correct)