Finding the Complement of Event E AGENDA: Do Now a) Write an example of each type of probability (classical, empirical, subjective) b) Find the sample space and probability of rolling a six-sided die and spinning a four-section spinner and getting the event “blue 3.” Is this a simple event? Brief review of finding classical probability Brief notes on Finding the Complement of Event E

Review of Classical Probability 𝑃 𝐸 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝑒𝑣𝑒𝑛𝑡 𝐸 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑝𝑎𝑐𝑒

Review of Classical Probability Example: You roll a six-sided die. Find the probability of each event. Event A: rolling a 3 Event B: rolling a 7 Event C: rolling a number less than 5 one chance out of 6 of rolling a 3, probability is 1/6 or .167 no chance of rolling a 7, probability is 0/6 or 0 There are 4 numbers less than 5 – probability is 4/6 or 2/3 or .667 Find sample space: when a six-sided die is rolled, the sample space consists of six outcomes: {1, 2, 3, 4, 5, 6} There are 6 different possible outcomes

Finding the Complement of Event E The complement of event E is the set of all outcomes in a sample space that are not included in event E. The complement of event E is denoted by E’ and is read as “E prime.” The event and its complement add up to a probability of 1

Finding the Complement of Event E Example: You roll a six-sided die. Find the COMPLEMENT of the probability of each event. Event A: rolling a 3 Event B: rolling a 7 Event C: rolling a number less than 5 Probability of Event A is 1/6, so Complement of Event A is 1 – 1/6 = 5/6 (0.833) Probability of Event B is 0/6, so Complement of Event C is 1 – 0 = 1 Probability of Event C is 2/3, so Complement of Event C is 1 – 2/3 = 1/3 (0.333)

Finding the Complement of Event E You Try! You survey a sample of 1000 employees at a company and record the age of each. The results are shown in the frequency distribution. If you randomly select another employee, what is the probability of the employee will be between 25 and 34 years old? What is the probability of randomly choosing an employee who is not between 25 and 34 years old? Employee ages Frequency, f 15 to 24 54 25 to 34 366 35 to 44 233 45 to 54 180 55 to 64 125 65 and over 42 𝑓 =1000