Seftion 7 - Probability And Statistics Flashcards
How can you find the probability of a something if all possible outcomes are equally likely
Number of ways for something to happen divided by the total number of possible outcomes
What does a sample space diagram do
Shows all the possible outcomes
Like a Punnett square
What’s the product rule
The number of ways to carry out a combination of activities equals the number of ways to carry out each activity multiples together
How do you work out relative frequency
Frequency divided by number of times you tried the experiment
Calculates estimate of probability for something biases
What happens to the accuracy when you do an experiment more times
The more times you do it, the more accurate your estimate of probability should be
What’s a frequency tree
You can record results - shows outcomes and then answers
How do you calculate expected frequency
Expected frequency of s result = probability X number of trials
Can estimate how many times you’d expect something to happen if you do it n times
The expected frequency is based on probability of the result happening
What’s an independent event
If one event happening doesn’t affect the probability of the other happening
What’s a dependant event
If one event happening does affect the probability of the other happening
The events are dependent
Tell me how to work out the probability of both events happening
If two events, call them a and b are independent then
P(a and b) = p(a) X p(b)
Tell m the formula for events a OR b happening
If events can happen together
P(a or b) = p(a) + p(b) - p(a and b)
What’s mutually exclusive
When two events can’t happen together
Tell me the formula for working out probability of event a or b happening when they can’t happen together
P(a or b) = p(a) + p(b)
What are the 4 key tree diagram facts
On any set of branches which meet at any point add to one
Multiply along the branches to get the end probabilities
Check your diagram - the end probabilities add to 1
To answer any question, add up relevant end probabilities
Tell me about “at least questions”
“At least, a certain number of things happening - easier to work out:
1 - probability of less than that number of things happening
Tell me about conditional probabilities
The conditional probability of a given b is the probability of event a happening given that event b happens
What’s the and rule for conditional probabilities
CONDITIONAL
P(a and b) = p(a) X p(b given a)
Tell me about conditional probabilities on tree diagrams
The probabilities on a set of branches will change depending on previous event
What’s a set in a Venn diagram
Collections of things - call things elements
Tell me about sets on Venn diagrams
Can be written in curly brackets
N(a) just means the number of elements in a set
In a Venn diagram each set is represented by a circle containing the elements of the set or the number of elements in the set
What’s a sample
A smaller group of the Desired population
Can apply those conclusions to whole populations
For a sample to be representative what must it be
A random sample - means every member of population has an equal chance of being in it
Big enough for size of population - bigger the sample the more reliable
How do you select a simple random sample
Assign a number to every member of populations
Create a list of random names
Match the random numbers to members of the population
Tell me the problems of a sample
A biased sample is one that doesn’t properly represent whole populations - to spot it think about: when, where and how it was taken,
How many members were in it
If certain groups excluded it’s not random and is biased
