Probability 1 4 2 6 8 9 3 5 7 1 Vocabulary: probability sample space chance likelihood certain likely equally likely unlikely event outcome experiment theoretical spinner die dice favourable fair bias random complement 2 6 8 9 3 5 7 1

What is Probability? Probability is the study of chance, or how likely something is to happen. Probabilities range from 0 (an impossible event) to 1 (a certain event). If things have an equal chance of happening, we call them equally likely outcomes. This continuum shows where probabilities fall: On the continuum, place in the correct positions: likely unlikely very unlikely certain Impossible very likely equally likely 2 5 4 11 13 3 6 10 14 1 15 8 7 9 12

Sample Space The sample space is a list of all possible outcomes. For a coin, we say the sample space is {heads, tails}, because there is no other possible outcome. 2 5 4 11 13 3 6 10 14 1 15 8 7 9 12

2 5 4 3 6 1 8 7 9 Theoretical Probability A pail contains eight red marbles, five blue marbles, six green marbles and three yellow marbles. If a single marble is chosen from the pail, what is the probability it will be red? Blue? Green? 𝑃 𝑅𝑒𝑑 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑑 𝑚𝑎𝑟𝑏𝑙𝑒𝑠 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑎𝑟𝑏𝑙𝑒𝑠 = 8 22 𝑃 𝐵𝑙𝑢𝑒 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑙𝑢𝑒 𝑚𝑎𝑟𝑏𝑙𝑒𝑠 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑎𝑟𝑏𝑙𝑒𝑠 = 𝑃 𝐺𝑟𝑒𝑒𝑛 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑟𝑒𝑒𝑛 𝑚𝑎𝑟𝑏𝑙𝑒𝑠 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑎𝑟𝑏𝑙𝑒𝑠 2 5 4 11 13 3 6 10 14 1 15 8 7 9 12

The complement The sum of the probabilities of all possible outcomes of a simple event is always 1. This can be used to simplify calculations (it is called using the complement). 2 5 4 11 13 3 6 10 14 1 15 8 7 9 12