Probability Trees!

Probability Trees Trees allow us to visually see all the possibility's in an random event.

Independent Events Two events are independent if the first event does not influence the other. Ex. Choosing a red marble putting it back and choosing a blue marble.

Dependent Events When the first event does influence the second event. EX. Choosing a red marble keeping it out of the bag and than choosing a blue marble.

Basic Counting Principal Multiplying the number of ways each step of an experiment can be completed. Ex. Eric has two pairs of pants, three shirts and two ties. How many ways can he dress. 2X3X2=12

Independent red blue First Choice Second Choice red blue red blue Tree diagrams can be used to help solve problems involving both dependent and independent events. The following situation can be represented by a tree diagram. Peter has ten coloured cubes in a bag. Three of the cubes are red and 7 are blue. He removes a cube at random from the bag and notes the colour before replacing it. He then chooses a second cube at random. Record the information in a tree diagram. Probability (Tree Diagrams)

Tree Diagrams Could make a list Could draw up a table Probability of two or more events 1 st Throw 2 nd Throw T HHHH H T TTT 1/2 OUTCOMES H,H H,T T,H T,T P(Outcome) P(H,H)=1/2x1/2=1/4 P(H,T)=1/2x1/2=1/4 P(T,H)=1/2x1/2=1/4 P(T,T)=1/2x1/2=1/4 Total P(all outcomes) = 1

3/9 6/9 7/10 3/10 2/9 7/9 1 st event 2 nd event 7 Red 3 Blue. Pick 2, without replacement. a) p(R,R) b) p(B,B) c) p(One of each) OUTCOMESP(Outcome) R,R R,B B,R B,B P(R,R)=42/90 P(R,B)=21/90 P(B,R)=21/90 P(B,B)=6/90 Total P(all outcomes) = 1

Probability Trees Example 1 A bag contains 6 red beads and 4 blues. 2 beads are picked at random without replacement. (i) Draw a probability tree diagram to show this information (ii) Calculate the probability of selecting both red beads (iii) Calculate the probability of picking one of each colour.