This problem explores probability as students find if one outcome is more or less likely to occur than another outcome.
Probability is an important concept in our society. It is the basis for the insurance and gambling industries as well as underpinning many crucial business and military decisions.
During this lesson students develop ways of being systematic in their presentation and organisation of material. This skill is important in situations where events are counted and we must ensure that they are counted only once. It is a useful general skill in much of mathematics (and in life) and ensures that nothing vital is missed or overlooked.
George has put three coins in a line on the table and covered them up. They may have heads up (H) or tails up (T). When he uncovers them what is most likely, that he will see three heads or two heads and a tail?
What other possibilities are there for George’s coins? Say which are least likely, most likely and which are equally likely.
It is more likely that George will have two heads and a tail than three heads: HHT, HTH and THH compared with HHH. Alternatively it is least likely that he will Have three heads.
The full range of possibilities is shown below.
HHT, HTH, THH;
HTT, THT, TTH;
Two heads and a tail and two tails and a head are more likely than three heads or three tails. On the other hand, three heads and three tails are equally likely. Similarly, two heads and a tail and two tails and a head are equally likely. Three heads (or three tails) are less likely than two tails and a head (or two heads and a tail).
(Note the systematic way that the various possibilities are written down. Start by considering heads. There is clearly only one arrangement that will give three heads. Next consider how we could have one tail and then try only one head. Finally consider all tails (or no heads).
Printed from https://nzmaths.co.nz/resource/three-coins-table at 5:19pm on the 20th January 2021