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Coins inquiry

P(2 heads and 2 tails) 
when you flip 4 coins 
P(1 head and 1 tail) 
when you flip 2 coins

Is it possible to change the number of heads and tails to make the statement equal? (e.g. 2 heads from 2 coins)

Is there a pattern if we compare P(1H, 1T) from 2 coins and P(2H, 2T) from 4 coins and P(3H, 3T) from 6 coins ...
1/2  6/16  20/64  70/256
Connection to Pascal's triangle

You can represent the outcomes from two coins in a 2-way table. How would we represent the outcomes for 3 coins and 4 coins in a table (3-d table).

Does the order matter? e.g Is 2H and 2T the same as 2T and 2H?

Alternative prompt 
P(2 heads and 2 tails) when you flip 4 coins = 
2 x P(1 head and 1 tail) when you flip 2 coins   
This prompt was devised by Nicola Stokes (a Head of Mathematics in East Sussex, UK). Nicola tried it out with her year 9 class. The students responded to the prompt by asking the questions and making the statements above. Nicola reports that the prompt "worked really nicely and all of the class chose to continue to investigate if the prompt was true as they couldn't immediately see that it wasn't." During the inquiry, the students developed fluency in constructing sample space diagrams and tree diagrams.

Prompt sheet
Promethean flipchart     download
Smartboard notebook    download
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