Covers the various sections relating to Probability and Counting Principles within the Mathematics syllabus. (Paper 1 section) Includes notes from the textbook, as we...
Probability
Probability - The chance or likelihood that an event will happen.
Certain an event will happen: P(event) = 1
Certain an event won’t happen: P(not event) = 0
Always lies between 0 and 1
Probability terminology:
Trial - Experiment or activity
Trial - Example: Throw a dice or toss a coins
Outcome - Result of a trial
Outcome - Example: Heads or tails or 1 or 2 or 3
Sample space - All possible outcomes of a trial
Sample space - n(S) = number of possible outcomes
Event (E) - Specific outcome
Event (E) - Example: Get heads or get an eve number
Event (E) - n(E) = Number of elements in the subset
Frequency - Relative (empirical), the probability we actually get by experiment or experience
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑢𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
Frequency - = 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠
Frequency - Theoretical, the expected probability if enough trials are conducted
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑢𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑡ℎ𝑎𝑡 𝑒𝑥𝑖𝑠𝑡
Frequency - = 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
Venn diagram terminology:
Venn diagram - A diagram using circles to represent sets
Venn diagram - Position or overlap indicate relationships between the sets
Element of - Belongs to a set
Element of - Symbol ∈
Subset - A ⊏ B (A is contained in B)
Subset - Set of natural numbers is a subset of the set of integers.
Universal set - The whole sample space represented by
Union - Belongs to A or to B
Union - Symbol ∪ (or)
Intersection - Belongs to A and B
Intersection - Symbol ∩ (and)
Complementary - A’, not A
Complementary - Sets must be mutually exclusive and exhaustive
, Empty set - No elements
Empty set - Symbol ∅
Disjoint - Sets with no elements in common, i.e. no intersection (mutually exclusive)
Events with intersections
p(a ∪ b) = p(a) + p(b) - p(a ∩ b)
Independent events
p(a ∩ b) = p(a) x p(b)
p(a ∪ b) = p(a) + p(b) - p(a) x p(b)
Non independent events
p(a ∩b) = p(a) x p(b l a)
Conditional probability
p(a ∩ b)
p(a | b) = p(b)
Mutually exclusive events
p(a ∪ b) = p(a) + p(b)
Note:
Mutually exclusive Independent
p(a and b) 0 p(a) x p(b)
p(a or b) p(a) + p(b) p(a) + p(b) - p(a) x p(b)
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller KirstenBarbour. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R50,00. You're not tied to anything after your purchase.
