Are the outcomes equally likely?

This formula only works when all outcomes are EQUALLY LIKELY 𝑃 𝑒𝑣𝑒𝑛𝑡 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑃 𝑒𝑣𝑒𝑛𝑡 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑜𝑐𝑐𝑢𝑟𝑒𝑛𝑐𝑒𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑣𝑒𝑛𝑡 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠 This formula only works when all outcomes are EQUALLY LIKELY But when the outcomes are NOT equally likely …

Example A:When Jenna goes to the farmers’ market, she usually buys bananas. The number of bananas she might buy and their probabilities are shown in the table below. Number of bananas 1 2 3 4 5 Probability 0.1 0.2 0.3 a) What is the probability that Jenna buys exactly 3 bananas? 𝑃 𝑒𝑥𝑎𝑐𝑡𝑙𝑦 3 𝑏𝑎𝑛𝑎𝑛𝑎𝑠 = 0.2 or 20 % b) What is the probability that Jenna does not buy any bananas? 0.1 or 10 % 𝑃 𝑛𝑜 𝑏𝑎𝑛𝑎𝑛𝑎𝑠 =

Number of bananas 1 2 3 4 5 Probability 0.1 0.2 0.3 c) What is the probability that Jenna buys more than 3 bananas? 𝑃 𝑛>3 = 0.2 + 0.3 = 0.5 or 50 % d) What is the probability that Jenna buys at least 3 bananas? 𝑃 𝑛≥3 = 0.2 + 0.2 + 0.3 = 0.7 𝑜𝑟 70 % e) What is the probability that Jenna does not buy exactly 3 bananas? 1 − 𝑃 𝑒𝑥𝑎𝑐𝑡𝑙𝑦 3 𝑏𝑎𝑛𝑎𝑛𝑎𝑠 0.2 0.1 + 0.1 + 0.1 + 0.2 0.8 + 0.3 = 0.8 𝑜𝑟 80%

Example B*: When Jenna goes to the farmers’ market, she also usually buys some broccoli. The possible number of heads of broccoli that she buys and the probabilities are given in the table. Number of heads of broccoli 1 2 3 4 Probability 1 12 1 6 5 12 1 4 a) What is the probability that Jenna buys exactly 3 heads of broccoli? b) What is the probability that Jenna does NOT buy exactly 3 heads of broccoli? c) What is the probability that Jenna buys more than 1 head of broccoli? d) What is the probability that Jenna buys at least 3 heads of broccoli?

Example B: Number of heads of broccoli 1 2 3 4 Probability 1 12 1 6 5 12 1 4 a) What is the probability that Jenna buys exactly 3 heads of broccoli? 1 4 𝑃 𝑒𝑥𝑎𝑐𝑡𝑙𝑦 3 = b) What is the probability that Jenna does NOT buy exactly 3 heads of broccoli? 1 12 + 1 6 + 5 12 + 1 12 1 4 1 − 𝑃 𝑛𝑜𝑡 3 = 4 1 12 + 12 + 5 12 + 1 12 2 4 − 4 1 3 4 = 9 12

Example B: Number of heads of broccoli 1 2 3 4 Probability 1 12 1 6 5 12 1 4 c) What is the probability that Jenna buys more than 1 head of broccoli? 5 12 1 4 1 12 𝑃 𝑛>1 = + + 12 + 12 + 12 5 3 1 9 12 3 4 = = d) What is the probability that Jenna buys at least 3 heads of broccoli? 3 12 + 12 1 1 3 1 4 1 12 4 12 𝑃 𝑛≥3 = + = =

Example C: Spinner that looks like a clock 1 5 𝑃 𝑟𝑒𝑑 = 𝑃 𝑔𝑟𝑒𝑒𝑛 = 12 12 4 1 3 2 1 6 𝑃 𝑦𝑒𝑙𝑙𝑜𝑤 = 𝑃 𝑏𝑙𝑢𝑒 = = = 12 12 NOT equal outcomes! Why did we use the formula?

1 Example C: 1 6 5 12 𝑃 𝑏𝑙𝑢𝑒 𝑜𝑟 𝑔𝑟𝑒𝑒𝑛 = + 2 12 + 12 5 7 12 = 1 12 Color Red Blue Green Yellow Probability 1 12 1 6 5 12 1 3 1 6 5 12 𝑃 𝑏𝑙𝑢𝑒 𝑜𝑟 𝑔𝑟𝑒𝑒𝑛 = + 2 12 + 12 5 7 12 = 1 12 𝑃 𝑛𝑜𝑡 𝑟𝑒𝑑 = 1 − 12 12 − 12 1 11 12 =