Question

1. consider the square spinner shown and assume all sections are the same size. an experiment consists of spinning the spinner one time.

a. how many possible outcomes are there in the experiment?

b. what are the possible outcomes of the experiment?

c. list the sample space for the experiment.

d. calculate ( p(b) ).

e. calculate ( p(\text{number}) ).

f. calculate ( p(\text{not a number greater than 10}) ).

Explanation:

Step1: Count total spinner sections

Count the distinct equal sections on the spinner: 4 sections.

Step2: Identify labeled outcomes

List the unique labels on each section: 3, 17, \(b\), 11.

Step3: Define sample space

Sample space is all unique outcomes: \(\{3, 17, b, 11\}\).

Step4: Calculate \(P(b)\)

Probability = favorable outcomes / total outcomes: \(P(b) = \frac{1}{4}\)

Step5: Calculate \(P(\text{number})\)

Count numerical outcomes (3,17,11): 3. Probability: \(P(\text{number}) = \frac{3}{4}\)

Step6: Calculate \(P(\text{not >10})\)

Identify outcomes not >10: 3, \(b\). Count = 2. Probability: \(P(\text{not >10}) = \frac{2}{4} = \frac{1}{2}\)

Answer:

a. 4
b. The possible outcomes are 3, 17, \(b\), and 11.
c. \(S = \{3, 17, b, 11\}\)
d. \(\frac{1}{4}\)
e. \(\frac{3}{4}\)
f. \(\frac{1}{2}\)