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