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(number).

f. calculate p(not a number greater than 10).

Explanation:

Step1: Count equal sections

The spinner has 4 equal sections.

Step2: Identify distinct outcomes

The sections are labeled 3, 17, b, 11.

Step3: Define sample space

Sample space = all unique outcomes.

Step4: Calculate P(b)

Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total outcomes}}$ = $\frac{1}{4}$

Step5: Calculate P(number)

Count numeric outcomes: 3,17,11 (3 total). Probability = $\frac{3}{4}$

Step6: Calculate P(not >10)

Numbers >10: 17,11 (2 outcomes). Outcomes not >10: 3, b (2 total). Probability = $\frac{2}{4}$ = $\frac{1}{2}$

Answer:

a. 4
b. 3, 17, b, 11
c. $\{3, 17, b, 11\}$
d. $\frac{1}{4}$
e. $\frac{3}{4}$
f. $\frac{1}{2}$