Page 32 - Math SL HB Sem 3

Probability

chance of something happening

Terms to know:

1) Experiment - a repeatable process that gives rise to various outmmes
2) Sample space, U - a list of all the possible outcomes

\ Exam p e

The sample space of throwing two fair dice
[1,u 17,21 t1,3] [1,4] t1,sl t1,61
12,11 12,21 t2,31 12,41 t2,sl lz,6)
t3,11 [3,2] t3,31 t3,41 t3,sl t3,61
l4,Ll 14,2\ [4,31 14,41 [4,s] [4,6]
ts,1l ts,2l [s,3] ts,4l ts,sl ts,6j
t6,11 16,21 t6,31 t6,41 t6,sl t6,61

The total number of possible outcomes, n(U) = 36

3) Event - a collection of the favourable possible outcomes

\. Exa mp

Two dice getting the same number: [1,1] ,12,21' 13,31, [4,4] , t5,5], t6,61

Probability:

Probability is defined as the number of outcomes favourable to an event, n(euent), over the total
number of all the possible outcomes, n(U). We may represent the probability of event A as:

n(A\
ia
P(A) _

\. Exa mple:

As seen from the Venn diagram, there are twelve points in the sample space and five points in
set ,4. Therefore,

n(A) s I
P (A) : I T I
n{U) 72
I I :
I I
, a
U

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