Question

1. a spinner is created with four equal sized sectors as shown. an experiment is run where the spinner is spun twice and the outcome is recorded each time.

a. create a sample space list of ordered pairs that represent the outcomes, such as (4, 2) which represents spinning a 4 on the first spin and a 2 on the second spin.
b. using your answer from a., determine the probability of obtaining two numbers with a sum of 4

Explanation:

Step1: List all possible pairs

Let the four - equal sized sectors be numbered 1, 2, 3, 4. The sample space of ordered pairs when the spinner is spun twice is:
$(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)$

Step2: Find pairs with sum 4

The pairs of numbers that sum to 4 are: $(1,3),(2,2),(3,1)$

Step3: Calculate probability

The total number of elements in the sample space $n(S)=16$. The number of favorable outcomes $n(E) = 3$.
The probability $P(E)=\frac{n(E)}{n(S)}=\frac{3}{16}$

Answer:

a. $(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),(3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)$
b. $\frac{3}{16}$