Probability Concepts Flashcards
What is Probability Concepts?
The probability of an event, X occurring is expressed as a decimal or a fraction from 0-1
How do we express the probability of an event occurring?
P(# of thing) = # of favourable outcomes / total # of outcomes
What does P(A n B) mean?
And
What does P(A/B) mean?
Out of
What does P(A u B) mean?
Or
What does P(A’) mean?
Not A
What does P(A u B/C) mean?
Or Out of
(A or B out of C)
How do we write: What is the probability of A or B?
P(A u B)
How do we write: What is the probability of A and B?
P(A n B)
How do we write: What is the probability of Everything but A?
P(A’)
How do we write: If B happens what is the probability of A?
P(A/B)
How would you write the probability for this question: If a student studies English what is the probability they study Psychology?
P(pyschology/english)
How do we write: What is the probability that A and B are ‘mutually exclusive’?
P(A n B) = 0
What does ‘mutually exclusive mean’?
If events A and B are mutually exclusive, either one happens or the other happens (they don’t both happen).
How do we write: What is the probability that 2 events are independent?
P(A n B) = P(A) x P(B)
What does it mean if events are independent?
If 2 events are independent i.e the outcome of one has no influence on the outcome of the other.
What is the ‘multiplication principle’?
When you want to know the probability of something happening you multiply the probabilities to find the total number of outcomes.
E.g if you roll 2 dice and want to know the probability of rolling 2 fives, you would multiply the probabilities of getting a five on each dice.
P(5,5) = 1/6 x 1/6 = 1/36
(note the 2 rolls are independent)
Using the ‘multiplication principle’ how would you answer this question: In year 10 students have 3 option lines.
1) Japanese, French, Te Reo.
2) Textiles, Food Tech
3) Graphics, D.I.T, Art, Hard Tech
How many different combinations are there?
3 x 2 x 4 = 24
Using the ‘multiplication principle’ how would you answer this question: If you roll 3 dice how many possible outcomes are there?
6 x 6 x 6 = 216
Using the ‘multiplication principle’ how would you answer this question: 5 people on a bench side by side. How many ways are there of arranging 5 people on a bench?
5 x 4 x 3 x 2 x 1 = 120
or 5! = 120
(! = factorial)
What is ‘experimental probability’?
When you use an experiment or past data to find a probability.
E.g In the last 56 games the All Blacks have won 43, therefore what is the probability they win their next game?
P(win) = 43/56 = 0.768 (3dp)
What is ‘theoretical probability’?
Probability that we can predict.
E.g Rolling a 3 when rolling a dice.
P(3) = 1/6
* the 1 is the 1 x 3 on dice
* the 6 is the total numbers on the dice
* P(X=3) means the same as P(3)
* P(X<4)=3/6=1/2(=0.5)
* P(X≥3)=4/6=2/3(=0.667(3dp))
If a card was drawn randomly from a deck what is the probability that it is a king?
P(X=king) = 4/52 = 1/13 = 0.077 (3dp)
If a card was drawn randomly from a deck what is the probability that it is a red card?
P(X=red card) = 1/2
If a card was drawn randomly from a deck what is the probability that it is a number less than or equal to 4?
P(X=≤ 4) = 16/52 = 4/13
If a card was drawn randomly from a deck what is the probability that it is a 6 and a club?
P(6 and club) = 1/52
If a card was drawn randomly from a deck what is the probability that it is a 3 or a heart?
P(3 or heart) = 16/52 = 4/13
What are the 3 things you need to do when working with probabilities?
- Know your TOTAL
- If using probabilities your total is 1. These might be displayed in a table or graph (probability distribution)
*If using frequencies (whole numbers) then make sure you know how many in total.
What are the 4 steps you do to answer this question: Let X=number of children in a household?
1) Draw the probability distribution table (remembering TOTAL MUST EQUAL 1).
2) Find the value of k
3) Draw a graph of the probability distribution
4) Then do all the calculations to get your answer
A group of Year 13’s were surveyed about their plans for the following year. Find the probability that: a. P(uni) b. P(uni u tech)
Plan Frequency
Uni 52
Tech 13
Trade 8
Job 9
Travel 11
Other 3
Total 96
What were the probabilities for each of the plans?
a. P(uni) = 52/96 = 13/24 (=-.54(2dp))
b. P(uni u tech) = 65/96 (=0.68(2dp))
Probabilities:
Uni: 52/96 = 0.54
Tech: 13/96 = 0.14
Trade: 8/96 = 0.08
Job: 9/96 = 0.09
Travel: 11/96 = 0.11
Other: 3/96 = 0.03
What is a two way table?
A Two way table also known as a table of counts has 2 variables in a group. The numerator is the top and the denominator is the total.
What is a Venn diagram?
3 interlocking circles used to help order our groups.
What is ‘relative risk’?
Relative Risk is used when comparing two probabilities, it is often referred to as finding true relative risk.
E.g If the probability of getting food poisoning from a food truck is 0.075 i.e P(food poisoning/food truck)=0.075 and the probability of food poisoning from a restaurant is 0.024 i.e P(food poisoning/restaurant)=0.024 then comparing these two; the relative risk or RR=P(A) / P(B)
so RR=0.075 / 0.024 = 3.1 (1dp) Therefore a person is 3.1 times AS likely to get food poisoning from a food truck than from a restaurant.
What are tree diagrams or probability trees?
Another tool to help calculate probabilities. It is useful when there is a sequence of events or when a group is split into subgroups then those subgroups are split again.
What are the 6 tips on tree diagrams?
1) Read left to right
2) Probabilities (decimals or fractions) on the branches
3) Outcomes at end of branches
4) Each set of branches contain probabilities that add to 1
5) Multiply across the branches to find the probability of a sequence of outcomes
6) Add favourable outcomes to answer a question
What is the equation for Expected Number?
probability x total
What is the equation for Independence?
P(A n B) = P(A) x P(B)
What is the equation for Mutually Exclusive?
P(A n B) = 0
What will a truly random sample be?
Unbiased
The bigger the sample the more _____________ you can have of your findings?
CONFIDENCE
what number is considered statistically sufficient as a sample size to make an inference?
30
What does a ‘random sample’ mean?
Each member of the population has the same chance of selection
Randomness in _____________ means events are _____________ of each other (i.e a previous outcome does not affect the probability that an event will occur).
- PROBABILITY
- INDEPENDENT
What is a Simulation?
A simulation imitates true probability using coins, cards, dice random number generator, spinners etc. It must be repeated a LOT of times.
