A very good way of working out complicated probability problems is to draw them. The best way of drawing them is to make a probability tree.

On a probability tree, lines split to show the different possible results. You label the ends of the lines with what could happen. You label the middle of each line with the probability of each happening.

This is the probability tree for flipping one coin.

Each split adds up to 1 for fractions 1 for decimals 100% for percentages

If you are drawing a tree for more than one thing, like rolling two dice, you tree will have two splits. One split after the other.

The probability tree is like a maze. You choose a path through it to get the results you want. Start on the left and move along the lines until you get to the right. To find the probability of those results multiply the numbers on the lines you use.

If more than one path gets you what you want then add up the results. Chance of 2 Heads = Chance of 2 Tails = Chance of 1 of each =

The probability tree shows the chances of different combinations when you flip a coin and then draw a card to see if it is a picture card. In a deck of cards there are 16 picture cards out of 52.

Sometimes the probabilities will change depending on what the first result is. e.g. You have a drawer with 10 socks in it, 7 red and 3 black. You draw out two socks, one at a time.

e.g. You have a drawer with 10 socks in it, 7 red and 3 black. You draw out two socks. What is the chance you draw out; a)2 Red Socks b)2 Black Socks c)1 Red Sock and 1 Black Sock

You have a bag with a bunch of coins in it. There are four $2 coins and six $1 coins. Draw a probability tree showing two coins drawn out at random. What is the chance of drawing out a total of;a)$2 b)$3 c)$4

You have a bag with a bunch of coins in it. There are four $2 coins and six $1 coins. Draw a probability tree showing three coins drawn out at random. What is the chance of drawing out a total of; a)$3 b)$4 c)$5 d)$6

Lotto strike requires you to get the first four balls drawn in order. The balls are numbered from 1 to 40. Draw a probability tree to show the chance of winning lotto strike. There will be ___ splits and each split will be between “Right Number” and “Wrong Number”. Make your probability tree big.