a fair spinner is shown. janelle spins the spinner arrow 150 times. match each outcome with the number of…

Answer:

• The letter C is spun: 25 times
• The letter A or E is spun: 50 times
• Any letter that is not E is spun: 125 times

Explanation:

Step1: Determine the probability of each outcome.

The spinner has 6 equally likely sections (A, B, C, D, E, F). The probability of landing on any specific letter is $\frac{1}{6}$.

• Probability of C: $P(C) = \frac{1}{6}$
• Probability of A or E: There are 2 favorable outcomes (A, E). So, $P(A \text{ or } E) = \frac{2}{6} = \frac{1}{3}$
• Probability of not E: There are 5 favorable outcomes (A, B, C, D, F). So, $P(\text{not } E) = \frac{5}{6}$

Step2: Calculate the expected number of occurrences for each outcome.

The total number of spins is 150. Expected occurrences = Probability of outcome $\times$ Total spins.

• Expected times C is spun: $$ E(C) = P(C) \times 150 = \frac{1}{6} \times 150 = 25 \text{ times} $$
• Expected times A or E is spun: $$ E(A \text{ or } E) = P(A \text{ or } E) \times 150 = \frac{1}{3} \times 150 = 50 \text{ times} $$
• Expected times any letter that is not E is spun: $$ E(\text{not } E) = P(\text{not } E) \times 150 = \frac{5}{6} \times 150 = 5 \times 25 = 125 \text{ times} $$