Probability Flashcards
What’s the definition of trial?
Number of times an experiment is conducted.
What’s the definition of outcome?
Result obtained from trial.
What’s the definition of event?
Desired or favourable outcome.
What’s the definition of sample space?
List of all the different possible outcomes of a trial. Represented by the letter S = {1, 2, 3, 4}
What’s the definition of bias?
1 outcome is unfairly favoured above others.
What’s the definition of probability?
Chance of an event occurring. Can be written as fractions, decimals, percentages or words.
What’s the formula for theoretical probability?
no. of favourable outcomes divided by no. of possible outcomes.
What’s the formula for expected and relative frequency?
Relative: Known frequency divided by the total number of trials.
Expected: Probability (as a decimal) x total no. of trials.
What is set notation and Venn diagrams?
Venn diagrams show all possible outcomes.
Each different sector or collection of data is called a set.
When combined, it makes a universal set (It contains all possible outcomes).
These are the symbols:
Pr(A) = Probability of A occurring.
Pr(A’) = Probability of A not occurring
Pr(AnB) = Probability of A and B just both occurring.
Pr(AuB) = Probability of A or B occurring everything within the circles.
What are mutually exclusive events?
If 2 events cannot possibly occur at the same time then the events are mutually exclusive.
For example, when tossing a die getting a 1 is mutually exclusive from getting a 5. You cant have both at once.
This is called the addition rule = P (A or B)
= P (A) + P (B)
=
What are complementary events?
The outcome that isn’t the desired or favourable event/outcome.
Formula: 1 - Pr(A) = Pr(A’)
Pr(A) is in decimal form.
What is independent and dependent (conditional) probability?
Independent events mean each event is not affected by other events.
This event has replacement.
For example, a coin has two outcomes and the chance of both outcomes are always 1/2 therefore the event of getting a tails is not affected by heads because there is always a 1/2 chance of getting your favourable outcome.
Formula for multiple independent events:
Pr(A∩B) = Pr(A)×Pr(B)
In decimal form.
Conditional Independence Formula: Pr(A∣B) = Pr(A)
Pr (BIA) = Pr (B).
Conditional probability is the probability of an event occurring given that an event has already occurred.
This event has no replacement.
Formula: Pr (AIB) = n(AnB) divide by n(B)
Pr (BIA) = n(AnB)/n(A)
n = number
What do tree diagrams look like with and without replacement?
LIST THE OUTCOMES
Without Replacement: A tree diagram at first has all the normal outcomes but as the second trial commences are not replaced so don’t put the ones already in there.
For example,
= R
= R
R = Y
= Y
R
R
Y =R
= R
= R
= Y
Y
As you can see there is two Y’s and in the first branch the Y was chosen out of all the other letters and then in the second branch the outcomes were the other three R’s or the final Y, this is what a tree diagram looks like without replacement.
With Replacement: A tree diagram is designed as normal every outcome is repeated as many times as there is trials.
If you had a Venn diagram and knew how many number of people were in part A and Part B of the diagram as the total number of people then how would you calculate how many like both?
1st Step: Plus Part A and Part B together.
2nd Step: Take Part A and B from the total number of people.
3rd Step: That’s how many people like both.
For example,
Part A = 15, Part B = 11, Total = 20
1: 15+11=26
2: 26-20=6
3: 6
Don’t forget to take 6 from 15 and 11 to complete the Venn diagram.
When do you add or multiply probabilities?
You add probabilities when the sentence uses an OR statement.
You multiply probabilities when the sentence uses an AND statement.
