This problem solving activity has a statistics focus.
For fun, Iosefa and Maru are dressing in the dark.
There are two red socks and two blue socks.
Are the boys more likely to get a pair, or one sock of each colour?
How do you know?
In this problem students should be encouraged to draw combinations, make a systematic list or table, or use equipment to show that they have explored all the possibilities.
The solution shows a systematic approach.
For fun, Iosefa and Maru are dressing in the dark. There are two red socks and two blue socks. Are the boys more likely to get a pair, or one sock of each colour?
How do you know?
The next day there are 5 socks to choose from. There are 3 blue socks and 2 red. Are the boys more likely to get odd socks or a pair? Show how you know.
The table represents Iosefa's choices. After all, if he chooses a pair, then so does Maru. And if Iosefa chooses a mixture, then so does Maru.
You will notice that in the table there are some blank spaces. This is because Iosefa can’t choose the first red sock (R1) and the first red sock (R1). He has to choose two different socks.
R1 | R2 | B1 | B2 | |
R1 | R1,R2 (pair) | R1,B1 | R1,B2 | |
R2 | R2,R1 (pair) | R2,B1 | R2,B2 | |
B1 | B1,R1 | B1,R2 | B1,B2 (pair) | |
B2 | B2,R1 | B2,R2 | B2,B1 (pair) |
From the table there are 12 possibilities for Iosefa. We have indicated the pairs. There are only 4 possible pairs. This means that Iosefa is more likely to get an ‘odd’ pair than a proper pair.
There is even less chance of the boys getting a pair of socks here. This is because in the extension there are 20 ways of choosing the socks and there are only 8 pairs possible.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/dressing-dark at 8:56pm on the 26th February 2024