Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers. If necessary, use / for the fraction bar(s).

Question

Brianna rolls a fair, six-sided die, and then spins the spinner shown below.

The probability of rolling an odd number and landing on
is .

The probability of rolling a 2 and landing on green or red is
.

The probability of rolling a prime number and not landing on blue is
.

Answer 1

To solve these problems, we need to calculate the probabilities based on the information provided about the die and the spinner.

1. The probability of rolling an odd number and landing on (spinner section):

• The odd numbers on a six-sided die are 1, 3, and 5. So there are 3 odd numbers out of 6 possible results.
• Assuming the spinner has sections that are equally likely, if we denote the total number of sections on the spinner as N and let P represent the chosen section, the probability of landing on P is 1/N.
• Therefore, the probability of rolling an odd number and landing on P is:

\[ P(\text{odd number and } P) = \left(\frac{3}{6}\right) \times \left(\frac{1}{N}\right) = \frac{3}{6N} = \frac{1}{2N} \]

2. The probability of rolling a 2 and landing on green or red:

• The probability of rolling a 2 is 1/6 (since there is only 1 way to roll a 2 out of 6).
• If we let G represent the green section and R the red section, we need to know how many sections are either green or red. Assuming there are G + R sections (for the respective colors) out of N total sections,
• The combined probability is given by:

\[ P(2 \text{ and green or red}) = \left(\frac{1}{6}\right) \times \left(\frac{G + R}{N}\right) \]

3. The probability of rolling a prime number and not landing on blue:

• The prime numbers on a six-sided die are 2, 3, and 5. So there are 3 prime numbers out of 6.
• If we denote the number of blue sections on the spinner as B, the probability of not landing on blue would then involve landing on the other sections (N - B).
• The combined probability is given by:

\[ P(\text{prime number and not blue}) = \left(\frac{3}{6}\right) \times \left(\frac{N - B}{N}\right) = \frac{1}{2} \times \frac{N - B}{N} = \frac{N - B}{2N} \]

Now, fill in the boxes accordingly:

• The probability of rolling an odd number and landing on P is 1/2N.
• The probability of rolling a 2 and landing on green or red is 1/6(G + R/N) (exact fractions will depend on actual G and R).
• The probability of rolling a prime number and not landing on blue is (N - B)/(2N).

Make sure to provide the actual values for G, R, and B based on your spinner.