a spinner contains four equally shaded areas, as shown below. louise spins the spinner twice. which…

Explanation:

First, let's determine the probability of landing on each color. The spinner has 4 equal areas: orange, blue, blue, green. So the probabilities for each color are:

• ( P(\text{orange}) = \frac{1}{4} )
• ( P(\text{blue}) = \frac{2}{4} = \frac{1}{2} )
• ( P(\text{green}) = \frac{1}{4} )

Since the spins are independent, we use the multiplication rule for independent events: ( P(A \text{ and } B) = P(A) \times P(B) )

Step 1: Check ( P(\text{both green}) )

( P(\text{green}) = \frac{1}{4} ), so ( P(\text{both green}) = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} ). This is correct.

Step 2: Check ( P(\text{both blue}) )

( P(\text{blue}) = \frac{1}{2} ), so ( P(\text{both blue}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} ). This is correct.

Step 3: Check ( P(\text{first green and then blue}) )

( P(\text{green}) = \frac{1}{4} ), ( P(\text{blue}) = \frac{1}{2} ), so ( P(\text{first green and then blue}) = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} ). The given value is ( \frac{1}{6} ), which is incorrect.

Step 4: Check ( P(\text{first orange and then blue}) )

( P(\text{orange}) = \frac{1}{4} ), ( P(\text{blue}) = \frac{1}{2} ), so ( P(\text{first orange and then blue}) = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} ). This is correct.

Step 5: Check ( P(\text{first orange and then green}) )

( P(\text{orange}) = \frac{1}{4} ), ( P(\text{green}) = \frac{1}{4} ), so ( P(\text{first orange and then green}) = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} ). The given value is ( \frac{1}{4} ), which is incorrect.

Answer:

The correct probabilities are:

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

So the correct options are:

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