Created by Mr Lafferty Maths Dept Probability Likelihood Number Line Combined Probabilities Relative Frequency www.mathsrevision.com Mutually Excusive Events Independent Events 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Starter Questions 75o xo www.mathsrevision.com 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Probability Learning Intention Success Criteria To understand probability in terms of the number line and calculate simple probabilities. Understand the probability line. www.mathsrevision.com Calculate simply probabilities. 18-Nov-18 Created by Mr Lafferty Maths Dept

Probability Likelihood Line 1 0.5 Impossible Evens Certain Not very likely Very likely www.mathsrevision.com Seeing a butterfly In July School Holidays Winning the Lottery Baby Born A Boy Go back in time 18-Nov-18 Created by Mr Lafferty Maths Dept

Probability Likelihood Line 1 0.5 Impossible Evens Certain Not very likely Very likely www.mathsrevision.com It will Snow in winter Homework Every week Everyone getting 100 % in test Toss a coin That land Heads Going without Food for a year. 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Probability Key Points To work out a probability P(A) = www.mathsrevision.com Probability is ALWAYS in the range 0 to 1 18-Nov-18 Created by Mr Lafferty Maths Dept

Probability Number Likelihood Line 1 2 3 5 4 7 6 8 1 0.5 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 Impossible Evens Certain www.mathsrevision.com 8 P = Q. What is the chance of picking a number between 1 – 8 ? = 1 8 4 Q. What is the chance of picking a number that is even ? P(E) = = 0.5 8 Q. What is the chance of picking the number 1 ? 1 P(1) = = 0.125 18-Nov-18 Created by Mr Lafferty Maths Dept 8

Probability Likelihood Line 52 cards in a pack of cards 1 0.5 0.1 0.2 0.3 0.4 0.6 0.7 0.8 0.9 Impossible Evens Certain Not very likely Very likely www.mathsrevision.com 26 Q. What is the chance of picking a red card ? P (Red) = = 0.5 52 13 Q. What is the chance of picking a diamond ? P (D) = = 0.25 52 4 Q. What is the chance of picking ace ? P (Ace) = = 0.08 52 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Probability S4 General Now try Ex 1A & 1B Ch10 (page 123) www.mathsrevision.com 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Starter Questions 37o xo www.mathsrevision.com 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Probability Combined Probabilities Learning Intention Success Criteria To understand combined probability by constructing tables or tree diagrams. Construct combination tables and tree diagrams. Calculate probabilities from tables or tree diagrams. www.mathsrevision.com 18-Nov-18 Created by Mr Lafferty Maths Dept

Probability www.mathsrevision.com Traffic Light 1 Traffic 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 2 Calculate Probability : Both green R A G r (r,R) (r,A) (r,G) www.mathsrevision.com Traffic Light 1 a (a,R) (a,A) (a,G) 2. At least one green g (g,R) (g,A) (g,G) 3. One is amber one red 18-Nov-18 Created by Mr Lafferty Maths Dept

Probability www.mathsrevision.com Traffic Light 1 Traffic Light 2 Combined Probabilities Another way of representing the data ! Tree Diagram R (r,R) Calculate Probability : Both green T L2 A (r,A) r G (r,G) R (a,R) a A T L 1 (a,A) 2. At least one green www.mathsrevision.com T L2 G (a,G) g 3. One is amber one red R (g,R) A (g,A) T L2 (g,G) G 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Probability Combined Probabilities Key Points List all combinations (using a suitable table or tree diagram) 2. Interpret information to calculate probabilities. www.mathsrevision.com 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Probability Combined Probabilities S4 General Now try Exercise 2 Ch10 (page 124) www.mathsrevision.com 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Starter Questions 120o xo www.mathsrevision.com 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Probability Relative Frequency Learning Intention Success Criteria To understand the term relative frequency. Know the term relative frequency. Calculate relative frequency from data given. www.mathsrevision.com 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Probability Relative Frequency Relative Frequency : How often an event happens compared to the total number of events. Example Daniel Frances Number of heads 24 55 Number of tosses 60 100 www.mathsrevision.com Joe has a R.F. of heads = 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Probability Relative Frequency Relative Frequency : How often an event happens compared to the total number of events. Example Daniel Frances Number of heads 24 55 Number of tosses 60 100 www.mathsrevision.com Frances has a R.F. of heads = 18-Nov-18 Created by Mr Lafferty Maths Dept

Probability www.mathsrevision.com Joe has a R.F. of heads = Relative Frequency Joe has a R.F. of heads = Frances has a R.F. of heads Whose relative frequency is closer to P(H) ? www.mathsrevision.com P(H) = 0.5 France’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 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Probability Relative Frequency S4 General Now try Exercise 3 Ch10 (page 126) www.mathsrevision.com 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Starter Questions 55o xo 47o www.mathsrevision.com 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Probability Mutually Exclusive Learning Intention Success Criteria To understand that the term mutually exclusive. Understand that we simply add probabilities with this property. Understand the term mutually exclusive. Calculate probabilities for events that have this property. www.mathsrevision.com 18-Nov-18 Created by Mr Lafferty Maths Dept

Probability www.mathsrevision.com P(A or B) = P(A) + P(B) Cannot happen at the same time Probability Mutually Exclusive When two events are MUTUALLY EXCLUSIVE we can simply add their individual probabilities P(A or B) = P(A) + P(B) www.mathsrevision.com “or” means add 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Probability Mutually Exclusive Example : There are 12 balls in a box. Q. What is the probability of picking a green ball. P(G) = www.mathsrevision.com Q. What is the probability of picking a white ball. P(W) = Q. What is the probability of picking a green OR white ball. P(G or W) = P(G) + P(W) 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Probability Mutually Exclusive S4 General Now try Ex 4A & 4B Ch10 (page 127) www.mathsrevision.com 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Starter Questions xo 270o www.mathsrevision.com 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Probability Independent Events Learning Intention Success Criteria To understand that if two events are independent we can simply multiply probabilities. Understand when two events are independent. Calculate probabilities for events that are independent. www.mathsrevision.com 18-Nov-18 Created by Mr Lafferty Maths Dept

Probability www.mathsrevision.com P(R,R) = P(R) x P(R) Spinner 1 Independent Events Calculate P(R) for spinner 1 Write down all the possible outcomes when the two spinners are spun together. Spinner 2 Calculate (R) for spinner 2 Y G R Y (Y,Y) (Y,G) (Y,R) www.mathsrevision.com Spinner 1 G (G,Y) (G,G) (G,R) R (R,Y) (R,G) (R,R) Notice from table P (R,R) P(R,R) = P(R) x P(R) 18-Nov-18 Created by Mr Lafferty Maths Dept

Probability Key Points www.mathsrevision.com P(A and B) = P(A) x P(B) Independent Events Key Points For two independent events A and B we can multiply the individual probabilities P(A and B) = P(A) x P(B) www.mathsrevision.com “and” means multiply Independent Events List all combinations. Calculate individual probabilities. Multiply them together. 18-Nov-18 Created by Mr Lafferty Maths Dept

Created by Mr Lafferty Maths Dept Probability Independent Events S4 General Now try Exercise 5 Ch10 (page 129) www.mathsrevision.com 18-Nov-18 Created by Mr Lafferty Maths Dept