Experimental The larger the number of trials Theoretical P(Heads) from one coin Tree diagrams A visual way of showing all the possible outcomes of two or more versus performed, the closer the toss = 0.5 events. theoretical experimental probability will get to 10 coin tosses produced 4 heads probability the theoretical probability Each branch leads to a possible outcome and is labelled with a probability. Experimental P(Heads) = 0.4 100 coin tosses produced 48 heads The sum of the probabilities of all branches from an event should Experimental P(Heads) = 0.48 be 1. 1000 coin tosses produced 495 heads Experimental P(Heads) = 0.495 Probabilities are multiplied along the branches (the AND rule) Frequency trees Used to record and organise information given as frequencies. A running club has 160 members. 74 of the club members are female. The sum of probabilities of all possible outcomes must add up to 1 58 of the female members are over 18. 21 of the male club members are under 18. Complete the frequency tree to show this information. (Do not confuse with Tree Diagrams) Draw a tree diagram to show all the possible outcomes of tossing a coin and a dice Sample space A visual way of recording all the possible outcomes of two events diagrams A sample space diagram to show all the possible outcomes of tossing a coin AND rolling a dice
Experimental versus theoretical probability The larger the number of trials performed, the closer the experimental probability will get to the theoretical probability Theoretical P(Heads) from one coin toss = 0.5 10 coin tosses produced 4 heads Experimental P(Heads) = 0.4 100 coin tosses produced 48 heads Experimental P(Heads) = 0.48 1000 coin tosses produced 495 heads Experimental P(Heads) = 0.495 Frequency trees Used to record and organise information given as frequencies. A running club has 160 members. 74 of the club members are female. 58 of the female members are over 18. 21 of the male club members are under 18. Complete the frequency tree to show this information. (Do not confuse with Tree Diagrams) Sample space diagrams A visual way of recording all the possible outcomes of two events A sample space diagram to show all the possible outcomes of tossing a coin AND rolling a dice Tree diagrams A visual way of showing all the possible outcomes of two or more events. Each branch leads to a possible outcome and is labelled with a probability. The sum of the probabilities of all branches from an event should be 1. Probabilities are multiplied along the branches (the AND rule) The sum of probabilities of all possible outcomes must add up to 1 Draw a tree diagram to show all the possible outcomes of tossing a coin and a dice
11-probability-ks4-final.docx