Probability models: Equally likely outcomes
PROBLEM: Suppose you spin a spinner with three equal sections (red, blue, and
yellow) two times.
(a) Give a probability model for this chance process:
(b)Define event A as spinning blue at least once. Find .

Problem:

(a) Give a probability model for this chance process:

1. Identify the Sample Space (S):
   Since the spinner has three equally likely sections—Red ®, Blue (B), and Yellow (Y)—each spin can result in one of these three outcomes. When spinning the spinner twice, the outcomes are ordered pairs representing the results of each spin.
2. Determine the Probability of Each Outcome:
   • Each section is equally likely, so the probability of landing on any one color in a single spin is .
   • Since the two spins are independent, the probability of any ordered pair is the product of the probabilities of each individual spin.
3. Probability Model:

   Outcome	Probability
   (R, R)
   (R, B)
   (R, Y)
   (B, R)
   (B, B)
   (B, Y)
   (Y, R)
   (Y, B)
   (Y, Y)

(b) Define event A as spinning blue at least once. Find .

1. Counting Favorable Outcomes:
   First, identify all outcomes in the sample space where at least one spin is Blue.
   There are 5 favorable outcomes.
2. Using the Complement Rule:
   Alternatively, it’s often easier to calculate the probability of the complementary event (event ) where no spins result in Blue, and then subtract from 1.
   • Event : Neither spin is Blue.
   The outcomes where neither spin is Blue are:
   There are 4 such outcomes.
   Therefore,

(b)