1. Probability
[ S3.1 Core Starter]
In a game of chance players have to select a bag and then select a ball at random from that bag. If it is a black ball they win. The players have no idea how many balls are in each bag.
Which of these bags gives (i) the best and (ii) the worst chance of winning?
(iii) Put the bags in order of likelihood of winning.
Be prepared to explain the reasons for your answers!
Preamble
Discussion of pupils’ route to their answers is crucial in order to expose any serious misconceptions (see below). Pupils may work in pairs or small groups and if possible should realise the need to change the fractions into decimals in order to compare the probabilities of their own volition.
Possible content
Calculating and comparing simple probabilities and converting fractions into decimals.
Resources
Calculators to convert fractions into decimals in order that the probabilities may be compared.
Solution/Notes
Gold gives highest probability and red the lowest. Pupils should be challenged if their reasons only involve there being more or less black balls in the gold or red bags.
Original Material © Cambridge University Press 2010
Red
Green
Blue
Gold
= 0.4 = =
= …
Original Material © Cambridge University Press 2010