frequency trees and percentages

a ppt is here

generalising probability GCSE questions

three probability questions, adpated from past GCSE (England) papers
thanks to the exam boards

exploring some examples and then maybe attempting some fairly demanding generalisations

a ppt is here

red and yellow spheres

picking twice, with replacement

a ppt is here

exploring whether or not you are more or less likely to obtain two spheres of the same colour (RR or YY) than two speres of different colours (RY or YR)

 or use a tree diagram

options with a total of 9 spheres still

various totals

you can just consider half of the diagram

is the fawn area larger or smaller than the red plus the yellow?

fold once

fold twice

approached algebraically

an alternative algebraic justification

utilising pythagoras to justify the result

two events, without replacement

two events, with replacement

a ppt is here

tree diagrams

squirrel

a ppt is here

this could be simulated, with three dice rolls (at most)
e.g. first throw: (1 , 2) = left, (3, 4) = middle, (5, 6) = right
etc.

rotate the tree through 90 degrees clockwise

how could this game be made fair?

unit fraction from consecutive amounts

combined events, without replacement

a ppt is here

with consecutive numbers of red and white counters (e.g. 8 red, 9 white)
when is the probability of obtaining two reds a unit fraction (1/k)?

it is reasonably easy to show that (n - 1) needs to be a factor of 6
this gives the four solutions, all of which are fairly small
so trial and improvement should obtain most if not all of the solutions

two reds fair game

how many red balls and how many yellow balls could you use to create a fair game?

there is one easy to obtain answer and then lots of difficult ones... that would be hard to find

students could be asked to show that the numbers below do provide for a fair game with P(R,R) = 1/2

the number of reds divided by the number of whites appears to tend to a limit...















a ppt is here