Post on 24-Dec-2015
Probability : Combined events 1
Objectives
When you have competed it you should
* know the addition rule
* know Venn diagram
* know the mutually exclusive events
Key terms: Addition rule, Mutually exclusive events, Venn diagram, Exhaustive events
Addition Rule
If A and B are any two events of the same experiment then the probability of A or B or both occurring is given by
P ( A or B or both ) = P(A) + P(B) - P(A and B)
P ( A B ) = P(A) + P(B) - P(AB)
ABA B
SVenn diagram
Example 1
Events A and B are such that P(A) = 0.6 , P(B) = 0.7 and P(AB) = 0.4.
P(A B) = P(A) + P(B) - P(A B)
Solutiom
Find P(A or B or both)
A B1 = 0.2 A1 B = 0.3A B = 0.4
P(A B) = 0.6 + 0.7 - 0.4 = 0.9
Mutually Exclusive Events
If an event A can occur or an event B can occur but not both A and B can occur, then the two events A and B are said to be mutually exclusive.
P(AB) = 0
P(A B) = P(A) + P(B)
BA
In a race the probability that Martin wins is 0.3, the probability that Ali wins is 0.25 and the probability that Chun wins is 0.2.
Example 2
Find probability that (a) Martin or Chun wins (b) neither Chun nor Ali wins .
Solution
P( Martin or Chun ) = P(Martin) + P(Chun)
P( Martin or Chun ) = 0.30 + 0.20 = 0.50
P(neither chun nor Ali) = 1 - P( Chun or Ali ) = 1 - ( 0.20 + 0.25 )
= 0.55
Example 3
Solution
Faulty Not Faulty
Machine A
Machine B
8 4
5 3
Tests are carried out on two machines A and B to assess the likelihood that each machine will produce a faulty component.
A component is chosen at random from those tested. Find the probability that the component chosen (i) is from machine A
(ii) is a faulty component from machine B
(i) 12/20 = 3/5 (ii) 5/20 = 1/20