Question i)
Firstly, there are 4
pairs of socks in the drawer, so a total of 8
individual socks in the drawer.
For the first sock which is chosen, it could be any sock in the drawer. It doesn't matter at this point. So therefore, Sock 1 has probability of 8/8.
After Sock 1 is chosen and removed from the drawer, there will only be 7 socks left in the drawer. Of these 7 socks in the drawer, there will 2 of each color sock but only 1 of the color sock which was removed.
Therefore, to get a matching pair, the probability would be 8/8 x 1/7. Since in probability all outcomes will add up to 1:
P(matching sock after 2) = 1 - P(non matching sock after 2) = 6/7
If you were to write this you would only have to write P(non matching) = 8/8 x 6/7 = 6/7 as required.
Question ii)
P(non matching sock after 3) = 8/8 x 6/7 x 4/6 = 4/7
The reason the 3rd term above, 4/6, is not 5/6 is because the third sock cannot be the same as the first OR second sock.
Question iii)
P(non matching sock after 3) = 4/7 from above
Since in probability all outcomes will add up to 1:
P(matching sock after 3) = 1 - P(non matching after 3 socks) = 3/7
You should aim to never have to use tree diagrams. Remember, in probability:
- The word AND is equivalent to multiplication
- The word OR is equivalent to addition
