Question

a spinner contains four equally shaded areas, as shown below.
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:

Determine individual sector probabilities

Using the Theoretical Probability knowledge point

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Evaluate independent compound probabilities

Using the Independent Events and Probability Multiplication Rule knowledge points

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Match with given options

Comparing the calculated values with the choices:

• \(P(\text{both green}) = \frac{1}{16}\) is correct.
• \(P(\text{both blue}) = \frac{1}{4}\) is correct.
• \(P(\text{first green and then blue}) = \frac{1}{6}\) is incorrect (should be \(\frac{1}{8}\)).
• \(P(\text{first orange and then blue}) = \frac{1}{8}\) is correct.
• \(P(\text{first orange and then green}) = \frac{1}{4}\) is incorrect (should be \(\frac{1}{16}\)).

Answer:

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