We continued our lecture on Probabilities.
We introduced the important concepts of dependant events and independant events. Dependant event is a group of outcomes where the outcomes depend on each other, while an independant event is a group of outcomes where the outcomes do not depend on each other.
If A and B are two independant events, then the probability of A and B happening is:
P(A and B) = P(A) * P(B)
If A and B are two dependant events, then the probability of A and B happening is:
P( A and B) = P(A) * P(B after A)
Important to note is that for dependant events, when A happens, it changes the outcome space so P(B after A) is no longer the same as P(B), that is, we need to take into consideration about A’s happening.
We further talk about the two importance concepts of Permutations and Combinations.
A Combination is a group of outcomes where the order does not matter. For example, mixing two kinds of paints taken from 4 possible paints. Because of fixing effect, picking Red first then Blue has the same result of picking Blue first then Red. So here the order of picking does not matter.
A Permutation is an arrangement of outcomes in which the order does matter. For example, picking two paints out of 4 possible pains with one paint for the background and the other paint for the design. Order here matters.
We introduced that concept of factorial of a natural number where it is the product of itself and all the natural numbers less than it. So 5! = 5*4*3*2*1. And in particular, we define 0! = 1.
With that we have the formulae to calculate number of permutations of taking r things out of possible n things as:
nPr = n! / (n-r)!
And the number of combinations of taking r things out of possible n things is:
nCr = n! / [(n – r)! * r!]
Homework is as follows:
http://blog.newtonchineseschool.org/wangweidong/files/2012/06/Math7_Spring_HW_L14.pdf