Probability JP Venn Diagrams A Venn diagram is
Probability • JP
Venn Diagrams A Venn diagram is a very useful way of visualising a problem. You should use a Venn diagram where you have 2 or 3 events, each of which have only 2 outcomes. A successful outcome is inside the circle. A Venn diagram with 2 events (A and B) will look like the following… A B A Venn diagram with 3 events (A, B and C) will look like the following… A B JP C
• History Pass Maths Pass 0. 9 - 0. 75 = 0. 15 0. 8 - 0. 75 = 0. 05 0. 75 1 – (0. 15 + 0. 75 +0. 05) = 0. 05 JP
Addition Rule JP • Think about this logically using a Venn diagram A C 0. 1 0. 3 0. 2 0. 4
Conditional Probability • If you know B has already happened, then these are your only possible outcomes, so must be the denominator. The numerator must be therefore be the probability that A happens as well as B. A B 0. 2 0. 4 0. 1 0. 3 JP
Tree Diagrams You should recall tree diagrams from GCSE maths. At A level you may be required to draw larger tree diagram and answer more difficult questions on it. Example: John has a box of 20 chocolates. 12 are dark chocolate and 8 are milk chocolate. John eats 2 sweets. Draw a tree diagram to represent this and find the probability that (a) both sweets are the same type, (b) given that the 2 nd chocolate was dark, the 1 st chocolate was dark. Route 2 nd 1 st JP Ex 5 E Q 1 -4, 5 G Q 2, 7
JP Independent and Mutually exclusive Events • In other words, using the addition rule, there is no intersection Ex 5 F Q 1, 2, 3 5 G Q 1, 4 pg 111 Q 10
- Slides: 7