Maths Tree Diagrams_1

Maths Tree Diagrams_1

1. AND rule: (P)probability(A and B) = P(A) X P(B)

2. Tree Diagrams: The diagram will look a bit like a crocodiles mouth. Above is an example, The probability a letter arrives the next day is 3/5. I post two letters. Calculate the probability that only ONE arrives the next day. So in the middle we have the two 6/25 because they are both one letter arriving and one letter not arriving. So to get the probability you add the relevant ones(6/25 + 6/25) to get the answer which is 12/25, so the probability that only one letter arrives us 12/25

3. Not all the branches are nessacsery. Quicker and simpler to draw only the branches you need.

   • For example if you go back to the probability of only 1 letter arriving, you know only to draw the branches that are did, didn't and didn't didn't or did,did.
     • So the answer is still 12/25 but it saved loads of time.

4. Conditional Probability - depends on what happened before E.g Liz catches a bus to the station then a train, the probability of the bus being late is 0.4. If the bus is late she catches the train with the probability of 0.5. If the bus is on time she catches the train with probability of 0.8. Find the probability that she catches her train.

   • So the answer is 0.20 + 0.48 = 0.68

5. May be as a decimal, fraction or percentage.

   • If Decimal, first part out of 0.10 e.g. if 0.7 then other branch is 0.3. Then second part out of 1 e.g. 0.60 + 0.40 = 1
   • If Fraction then out of bottom number e.g 6/12 is 6 out of 12
   • If Percentage then out of 100

6. Without Replacement Problems. Not putting fist choice back affects probability of second choice.

   • E.g There are 6 fiction and 4 non-fiction books on a shelf. I take 2 books at random. Find the probability I have one of each.
     • So the answer is 24/90 + 24/90 = 48/90

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