 A tree diagram can be used to show the flow of the process.
 It is used to organise and calculate the probability of an event happening.



Example 





Event of an experiment: 


Definition 





Event is a set of possible outcomes that fulfill certain conditions for a sample space and is a subset for the sample space.




Probability of an event: 

 The number of possible outcomes is represented by \(n(S)\) .
 The number of events is represented by \(n(A)\).
 The probability of an event \(A\) is \(P(A)\).


Then, the probability of an event \(A\) is represented by
\(P(A) = \dfrac{n(A)}{n(S)}.\)


13.3 
Complement of An Event Probability 

The probability for the complement of an event, \(P(A')\)
\(\begin{aligned} P(A) + P(A') &= 1 \\\\ P(A') &= 1 P (A) \\\\ \end{aligned}\)
where \(0 \le P(A) \le 1\).


13.4 
Simple Probability 


Example 





A box contains \(8\) green balls, \(12\) black balls and a number of white balls.
A white ball is chosen at random from the box.
The probability of getting a white ball is \(\dfrac{3}{7}\).
What is the number of white balls in the box?






Let \(w\) be the number of white balls.
Then,
\(\begin{aligned}n(S)&=8+12+w\\\\&=20+w.\\\\\end{aligned}\)
So,
\(\begin{aligned} P(w)&=\dfrac{n(w)}{n(S)} \\\\\dfrac{3}{7}&=\dfrac{w}{20+w} \\\\3(20+w)&=7(w) \\\\60+3w&=7w \\\\4w&=60 \\\\w&=15.\\\\ \end{aligned}\)
Thus, the number of white balls in the box is \(15\).



