1 / 7

Probability & Tree Diagrams

Probability & Tree Diagrams. OCR Stage 8. What are Tree Diagrams. A way of showing the possibilities of two or more events Simple diagram we use to calculate the probabilities of two or more events . Possible Outcomes. For example – a fair coin is spun twice. 1 st. 2 nd. H. HH. H. T.

diella
Download Presentation

Probability & Tree Diagrams

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Probability & Tree Diagrams OCR Stage 8

  2. What are Tree Diagrams • A way of showing the possibilities of two or more events • Simple diagram we use to calculate the probabilities of two or more events

  3. Possible Outcomes For example – a fair coin is spun twice 1st 2nd H HH H T HT H TH T T TT

  4. Attach probabilities 1st 2nd H HH P(H,H)=½x½=¼ ½ H ½ ½ T HT P(H,T)=½x½=¼ H TH ½ P(T,H)=½x½=¼ ½ T ½ T TT P(T,T)=½x½=¼ INDEPENDENT EVENTS – 1st spin has no effect on the 2nd spin

  5. Calculate probabilities 1st 2nd * H HH P(H,H)=½x½=¼ ½ H ½ ½ * T HT P(H,T)=½x½=¼ * H TH ½ P(T,H)=½x½=¼ ½ T ½ T TT P(T,T)=½x½=¼ Probability of at least one Head?

  6. For example – 10 coloured beads in a bag – 3 Red, 2 Blue, 5 Green. One taken, colour noted, returned to bag, then a second taken. 1st 2nd R RR B RB R G RG INDEPENDENT EVENTS R BR BB B B G BG R GR G GB B G GG

  7. All ADD UP to 1.0 Probabilities 1st 2nd R RR P(RR) = 0.3x0.3 = 0.09 0.3 0.2 B RB P(RB) = 0.3x0.2 = 0.06 R 0.3 G 0.5 RG P(RG) = 0.3x0.5 = 0.15 R BR P(BR) = 0.2x0.3 = 0.06 0.3 0.2 0.2 BB P(BB) = 0.2x0.2 = 0.04 B B 0.5 G BG P(BG) = 0.2x0.5 = 0.10 R GR P(GR) = 0.5x0.3 = 0.15 0.3 0.5 G 0.2 GB P(GB) = 0.5x0.2 = 0.10 B G GG P(GG) = 0.5x0.5 = 0.25 0.5

More Related