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GCSE Mathematics

GCSE Mathematics. Probability and Data Handling. Probability. The probability of any event lies between 0 and 1. 0 means it will never happen. 1 means it is certain to happen. Between these values, the event may or may not happen. The sum of all probabilities is equal to 1. Probability.

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GCSE Mathematics

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  1. GCSE Mathematics Probability and Data Handling

  2. Probability • The probability of any event lies between 0 and 1. • 0 means it will never happen. • 1 means it is certain to happen. • Between these values, the event may or may not happen. • The sum of all probabilities is equal to 1

  3. Probability • The probability of one event happening OR another is found by adding the probabilities, being careful of any overlap • The probability of one event happening AND another happening is found by multiplying the probabilities, being careful of replacement

  4. Find the following probabilities P(B) =1/11 P(U) =2/11 P(Vowel) =5/11 So P(consonant) =1 - 5/11=6/11 P(U or R) =2/11 + 1/11=3/11 P(Vowel or red) =5/11 +5/11 - 3/11 =7/11 BO UR NE MO U T H

  5. One letter is chosen, replaced, then another is chosen. P(2 B’s) =1/11 x1/11= 1/121 P( M then U) =1/11 x 2/11= 2/121 P(2 reds) =5/11 x 5/11= 25/121 Two letters are chosen without replacement P( 2 O's) =2/11 x 1/10=2/110 P( M then U) =1/11 x 2/10= 2/110 P(2 reds) =5/11 x 4/10= 2/11 BO UR NE MO U T H

  6. Possibility Space • Used to show all the outcomes of an event. • Two tetrahedral dice are thrown, one contains the numbers 0 2 4 6, the other contains the numbers 1 2 3 4. The score is found by adding the numbers together

  7. 0 2 4 6 1 1 3 5 7 2 2 4 6 8 3 3 5 7 9 4 4 6 8 10 P(8) = 2/16=1/8 P( odd number) = 8/16= 1/2 P( less than 5) = 6/16= 3/8 P( 4 or 9) = 2/16 + 1/16=3/16 Possibility Space

  8. Probability Trees • These are used when more than one event is being described. • They conveniently display ALL the possible outcomes. • Within a branch the probabilities add up to 1. • To calculate the given probability, multiply along the branches.

  9. Example • On my way to work I pass two sets of traffic lights. • The probability I have to stop at the first set is 0.4 • The probability I have to stop at the second set is 0.45 • What is the probability I have to stop (i) once only; (ii) at least once?

  10. s ss s g sg s gs g g gg 1st 2nd Outcome 0.4x0.45=0.18 0.4x0.55=0.22 0.6x0.45=0.27 0.6x0.55=0.33 Example

  11. Outcome 0.4x0.45=0.18 ss 0.4x0.55=0.22 sg 0.6x0.45=0.27 gs 0.6x0.55=0.33 gg P(stop once only) =0.22 +0.27 =0.47 P(Stop at least once) = 0.22+0.27+0.18 =0.67 OR 1-0.33 = 0.67 Example

  12. Time taken to get to college

  13. Histogram • As the data is continuous there should be no gaps. • Each bar should be the same width

  14. Pie Chart • Working out: • 6/30 x 360 =72 ° • 8/30 x360 = 96 ° • 14/30 x 360 = 168 ° • 2/30 x 360 = 24°

  15. Mean: Take the midpoint as the value of x x f fx 5 6 30 15 8 120 25 14 350 35 2 70 Mean= (30 + 120 + 350 + 70)/30 =570/30 =19 minutes NOT 570/4 = 142.5 Mean

  16. Median • Use a cumulative frequency curve. • USE THE UPPER VALUE • x f C.F. • 10 6 6 • 20 8 14 • 30 14 28 • 40 2 30

  17. Median and Interquartile Range • Median =21 minutes • Lower Quartile = 12 • Upper Quartile = 26 • Interquartile range • = 26 - 12 • =14

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