# S4 General 12-Apr-15 Likelihood Number Line Combined Probabilities Relative Frequency Probability www.mathsrevision.com Mutually Excusive Events Independent.

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S4 General 12-Apr-15 Likelihood Number Line Combined Probabilities Relative Frequency Probability www.mathsrevision.com Mutually Excusive Events Independent Events

S4 General 12-Apr-15 Starter Questions www.mathsrevision.com 75 o xoxo

S4 General 12-Apr-15 Probability Learning Intention Success Criteria 1.Understand the probability line. 1.To understand probability in terms of the number line and calculate simple probabilities. 2.Calculate simply probabilities. www.mathsrevision.com

S4 General 12-Apr-15 Probability Likelihood Line www.mathsrevision.com 10.50 CertainEvensImpossible Not very likely Very likely Winning the Lottery School Holidays Baby Born A Boy Seeing a butterfly In July Go back in time

S4 General 12-Apr-15 Probability Likelihood Line www.mathsrevision.com 10.50 CertainEvensImpossible Not very likely Very likely Everyone getting 100 % in test Homework Every week Toss a coin That land Heads It will Snow in winter Going without Food for a year.

S4 General 12-Apr-15 Probability www.mathsrevision.com Key Points To work out a probability P(A) = Probability is ALWAYS in the range 0 to 1

S4 General 12-Apr-15 Probability Number Likelihood Line www.mathsrevision.com 10.50 CertainEvensImpossible 12354 7 68 0.10.20.30.40.60.70.80.9 Q. What is the chance of picking a number between 1 – 8 ? Q. What is the chance of picking a number that is even ? Q. What is the chance of picking the number 1 ? 8 8 = 1 4 8 = 0.5 1 8 = 0.125 P = P(E) = P(1) =

S4 General 12-Apr-15 Probability Likelihood Line 10.50 CertainEvensImpossible Not very likely Very likely Q. What is the chance of picking a red card ? Q. What is the chance of picking a diamond ? Q. What is the chance of picking ace ? 52 = 0.5 13 52 = 0.25 4 52 = 0.08 26 0.10.20.30.40.60.70.80.9 P (Red) = P (D) = P (Ace) = 52 cards in a pack of cards

12-Apr-15 Now try Ex 1A & 1B Ch10 (page 123) www.mathsrevision.com Probability S4 General

12-Apr-15 Starter Questions www.mathsrevision.com 37 o xoxo

S4 General 12-Apr-15 Probability Learning Intention Success Criteria 1.Construct combination tables and tree diagrams. 1.To understand combined probability by constructing tables or tree diagrams. 2.Calculate probabilities from tables or tree diagrams. Combined Probabilities

S4 General 12-Apr-15 Calculate Probability : 1.Both green Probability www.mathsrevision.com Traffic Light 1Traffic Light 2 Combined Probabilities On route to school I pass two sets of traffic light. They work independently. Complete the table of all possible combinations Traffic Light 1 Traffic light 2 (r,R) (g,R) (a,R) (r,A) (g,A) (a,A) (r,G) (g,G) (a,G) AGR a g r 2. At least one green 3. One is amber one red

S4 General 12-Apr-15 Calculate Probability : 1.Both green Probability www.mathsrevision.com Traffic Light 1Traffic Light 2 Combined Probabilities Another way of representing the data ! Tree Diagram T L 1 (r,R) (g,R) (a,R) (r,A) (g,A) (a,A) (r,G) (g,G) (a,G) A G R a g r 2. At least one green 3. One is amber one red A G R A G R T L2

S4 General 12-Apr-15 Probability www.mathsrevision.com Key Points 1.List all combinations (using a suitable table or tree diagram) 2.Interpret information to calculate probabilities. Combined Probabilities

12-Apr-15 Now try Exercise 2 Ch10 (page 124) www.mathsrevision.com Probability S4 General Combined Probabilities

S4 General 12-Apr-15 Starter Questions www.mathsrevision.com 120 o xoxo

S4 General 12-Apr-15 Probability Learning Intention Success Criteria 1.Know the term relative frequency. 1.To understand the term relative frequency. 2.Calculate relative frequency from data given. www.mathsrevision.com Relative Frequency

S4 General 12-Apr-15 Probability www.mathsrevision.com Relative Frequency : How often an event happens compared to the total number of events.DanielFrances Number of heads 2455 Number of tosses 60100 Example Joe has a R.F. of heads = Relative Frequency

S4 General 12-Apr-15 Probability www.mathsrevision.com Relative Frequency : How often an event happens compared to the total number of events.DanielFrances Number of heads 2455 Number of tosses 60100 Example Frances has a R.F. of heads = Relative Frequency

S4 General 12-Apr-15 Probability www.mathsrevision.com Frances has a R.F. of heads Joe has a R.F. of heads = Whose relative frequency is closer to P(H) ? P(H) = 0.5France’s R.F. is closer to P(H) Note : The larger the random sample, the closer the relative frequency is to the probability of the event Relative Frequency

12-Apr-15 Now try Exercise 3 Ch10 (page 126) www.mathsrevision.com Probability S4 General Relative Frequency

S4 General 12-Apr-15 Starter Questions www.mathsrevision.com 55 o xoxo 47 o

S4 General 12-Apr-15 Probability Learning Intention Success Criteria 1.Understand the term mutually exclusive. mutually exclusive. 1.To understand that the term mutually exclusive. Understand that we simply add probabilities with this property. 2.Calculate probabilities for events that have this property. www.mathsrevision.com Mutually Exclusive

S4 General 12-Apr-15 Probability www.mathsrevision.com P(A or B) = P(A) + P(B) Mutually Exclusive When two events are MUTUALLY EXCLUSIVE Cannot happen at the same time we can simply add their individual probabilities “or” means add

S4 General 12-Apr-15 Probability www.mathsrevision.com Example : There are 12 balls in a box. Mutually Exclusive Q.What is the probability of picking a green ball. Q.What is the probability of picking a white ball. Q.What is the probability of picking a green OR white ball. P(G) = P(W) = P(G or W) = P(G) + P(W)

12-Apr-15 Now try Ex 4A & 4B Ch10 (page 127) www.mathsrevision.com Probability S4 General Mutually Exclusive

S4 General 12-Apr-15 Starter Questions www.mathsrevision.com xoxo 270 o

S4 General 12-Apr-15 Probability Learning Intention Success Criteria 1.Understand when two events are independent. 1.To understand that if two events are independent we can simply multiply probabilities. 2.Calculate probabilities for events that are independent. www.mathsrevision.com Independent Events

S4 General 12-Apr-15 Calculate P(R) for spinner 1 Probability www.mathsrevision.com Spinner 1Spinner 2 Independent Events Write down all the possible outcomes when the two spinners are spun together. Spinner 1 Spinner 2 (Y,Y) (R,Y) (G,Y) (Y,G) (R,G) (G,G) (Y,R) (R,R) (G,R) GRY G R Y Calculate (R) for spinner 2 Notice from table P (R,R) P(R,R) = P(R) x P(R)

S4 General 12-Apr-15 Probability www.mathsrevision.com Key Points For two independent events A and B we can multiply the individual probabilities P(A and B) = P(A) x P(B) 1.List all combinations. 2.Calculate individual probabilities. 3.Multiply them together. Independent Events “and” means multiply Independent Events

12-Apr-15 Now try Exercise 5 Ch10 (page 129) www.mathsrevision.com Probability S4 General Independent Events

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