Probability-Tree-Diagrams Wjec-Eduqas Foundation

课 Progress

0% Complete

Exam code:C300

Tree diagrams

How do I draw a tree diagram?

Tree diagrams can be used for repeated experiments with two outcomes
- The 1st experiment has outcome A or not A
- The 2nd experiment has outcome B or not B
Read the tree diagram from left to right along its branches
- For example, the top branches give A followed by B
  - This is called A and B

How to set up a tree diagram for two experiments each with two possible outcomes

How do I find probabilities from tree diagrams?

Write the probabilities on each branch
- Remember that P(not A) = 1 – P(A)
  - Probabilities on each pair of branches add to 1
Multiply along the branches from left to right
- This gives P(1st outcome and 2nd outcome)
Add between the separate cases
- For example
  - P(AA or BB) = P(AA) + P(BB)
The probabilities of all possible cases add to 1
If asked to find the probability of at least one outcome, it is quicker to do 1 – P(none)

Examiner Tips and Tricks

When multiplying along branches with fractions, don’t cancel fractions in your working – having the same denominator makes them easier to add together!

Worked Example

A worker drives through two sets of traffic lights on their way to work.
Each set of traffic lights has only two options: green or red.
The probability of the first set of traffic lights being on green is $5 over 7$ .
The probability of the second set of traffic lights being on green is $8 over 9$ .

(a) Draw and label a tree diagram. Show the probabilities of every possible outcome.

Work out the probabilities of each set of traffic lights being on red, R
Use P(red) = 1 – P(green)

$straight P open parentheses 1 to the power of st space straight R close parentheses equals 1 minus straight P open parentheses 1 to the power of st space straight G close parentheses equals 1 minus 5 over 7 equals 2 over 7$
<img alt=”straight P open parentheses 2 to the power of nd space straight R close parentheses equals 1 minus straight P open parentheses 2 to the power of nd space straight G close parentheses equals 1 minus 8 over 9 equals 1 over 9″ data-mathml='<math ><semantics><mrow><mi mathvariant=”normal” >P</mi><mfenced ><mrow><msup><mn>2</mn><mi>nd</mi></msup><mo> </mo><mi mathvariant=”normal”>R</mi></mrow></mfenced><mo >=</mo><mn >1</mn><mo >-</mo><mi mathvariant=”normal” >P</mi><mfenced ><mrow><msup><mn>2</mn><mi>nd</mi></msup><mo> </mo><mi mathvariant=”normal”>G</mi></mrow></mfenced><mo >=</mo><mn >1</mn><mo >-</mo><mfrac ><mn>8</mn><mn>9</mn></mfrac><mo >=</mo><mfrac ><mn>1</mn><mn>9</mn></mfrac></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ data-type=”working” height=”47″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2247%22%20width%3D%22259%22%20wrs%3Abaseline%3D%2230%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%20mathcolor%3D%22%23000000%22%20mathvariant%3D%22normal%22%3EP%3C%2Fmi%3E%3Cmfenced%20mathcolor%3D%22%23000000%22%3E%3Cmrow%3E%3Cmsup%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3End%3C%2Fmi%3E%3C%2Fmsup%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmi%20mathvariant%3D%22normal%22%3ER%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3Cmo%20mathcolor%3D%22%23000000%22%3E%3D%3C%2Fmo%3E%3Cmn%20mathcolor%3D%22%23000000%22%3E1%3C%2Fmn%3E%3Cmo%20mathcolor%3D%22%23000000%22%3E-%3C%2Fmo%3E%3Cmi%20mathcolor%3D%22%23000000%22%20mathvariant%3D%22normal%22%3EP%3C%2Fmi%3E%3Cmfenced%20mathcolor%3D%22%23000000%22%3E%3Cmrow%3E%3Cmsup%3E%3Cmn%3E2%3C%2Fmn%3E%3Cmi%3End%3C%2Fmi%3E%3C%2Fmsup%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmi%20mathvariant%3D%22normal%22%3EG%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3Cmo%20mathcolor%3D%22%23000000%22%3E%3D%3C%2Fmo%3E%3Cmn%20mathcolor%3D%22%23000000%22%3E1%3C%2Fmn%3E%3Cmo%20mathcolor%3D%22%23000000%22%3E-%3C%2Fmo%3E%3Cmfrac%20mathcolor%3D%22%23000000%22%3E%3Cmn%3E8%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3C%2Fmfrac%3E%3Cmo%20mathcolor%3D%22%23000000%22%3E%3D%3C%2Fmo%3E%3Cmfrac%20mathcolor%3D%22%23000000%22%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E9%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math143f4d31b04031e49f5eb18baba’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADxjdnQgDVUNBwAAAVgAAAA6Z2x5ZoPi2VsAAAGUAAAA%2FGhlYWQQC2qxAAACkAAAADZoaGVhCGsXSAAAAsgAAAAkaG10eE2rRkcAAALsAAAADGxvY2EAHTwYAAAC%2BAAAABBtYXhwBT0FPgAAAwgAAAAgbmFtZaBxlY4AAAMoAAABn3Bvc3QB9wD6AAAEyAAAACBwcmVwa1uragAABOgAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACgAAAAGAAQAAQACAD0iEv%2F%2FAAAAPSIS%2F%2F%2F%2FxN3wAAEAAAAAAAAAAAFUAywAgAEAAFYAKgJYAh4BDgEsAiwAWgGAAoAAoADUAIAAAAAAAAAAKwBVAIAAqwDVAQABKwAHAAAAAgBVAAADAAOrAAMABwAAMxEhESUhESFVAqv9qwIA%2FgADq%2FxVVQMAAAIAgADrAtUCFQADAAcAZRgBsAgQsAbUsAYQsAXUsAgQsAHUsAEQsADUsAYQsAc8sAUQsAQ8sAEQsAI8sAAQsAM8ALAIELAG1LAGELAH1LAHELAB1LABELAC1LAGELAFPLAHELAEPLABELAAPLACELADPDEwEyE1IR0BITWAAlX9qwJVAcBV1VVVAAEAgAFVAtUBqwADADAYAbAEELEAA%2FawAzyxAgf1sAE8sQUD5gCxAAATELEABuWxAAETELABPLEDBfWwAjwTIRUhgAJV%2FasBq1YAAQAAAAEAANV4zkFfDzz1AAMEAP%2F%2F%2F%2F%2FWOhNz%2F%2F%2F%2F%2F9Y6E3MAAP8gBIADqwAAAAoAAgABAAAAAAABAAAD6P9qAAAXcAAA%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

Maths Gcse Wjec-Eduqas Foundation