Counting Principles: Probability

Methods in this video

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1. 1

   Count the whole, then the ones that fit

   ▶ 0:48

   When to use it: The question asks which event is more likely, whether two are equally likely, whether something is certain or possible, or what the chance or probability is as a fraction; you can work out how many of each thing are in the bag, box, spinner or set of cards, and one is taken without looking (at random).

   • Probability = how many you want ÷ how many there are altogether; count the whole one by one: one disc, one card, one cell.
   • Certain = all of them are what you want; possible = not zero; equally likely = the same number; when the two groups are different sizes, compare fractions, not counts.
   • Taking one from each of two bags: draw a pairing grid with a × b cells; red–blue and blue–red are two different cells.
2. 2

   Work back from the chance

   ▶ 5:30

   When to use it: The question gives a probability as a fraction and asks how many of one kind are in the bag, how many there are altogether, or how many were added or taken out (How many … are in the bag? / How many … did she add?).

   • Given the chance, work back: how many you want = the whole × the probability; the rest = the whole minus what you know.
   • If the whole is not given, split the bag into as many equal parts as the denominator and use the parts you know to find one part.
   • The fraction is of the whole bag, not of the part shown in the graph.