PROBABILTY
COMPOUNDED EVENTS
In general, a compound event consists of two or more simple events. Tossing a dice is a simple event;
but tossing two dices or coins is a compound event.
Let’s toss two coins. Here are all the possible outcomes.
COMPLEMENT OF AN EVENT
Adopting this into probability,
The probability of getting the smallest number when a die is rolled: 1/6
The probability of getting the other numbers when a die is rolled: 5/6
So we can conclude that the possibility of an event A not occurring can be evaluated as = P(A’) = 1 – P(A)
Example
The probability of hitting the target of a bowman is 2/5 .What is the probability of the bowman missing the shot?
P(A)+ P(A') = 1
2/5+x=1
x=1-2/5=3/5
MUTUALLY EXCLUSIVE EVENTS
There are times when two events cannot happen at the same time.
P (A or B) = P (A) + P (B)
Example
When tossing a die, what is the probability of tossing a 2 or a 5?
n(A) =6
4+3+2=9 (sample space)
P(R)+P(B) 4/9+3/9 =7/9
MUTUALLY INCLUSIVE EVENTS
When two events can occur at the same time, they are inclusive.
P(A or B) = P(A) + P(B) − P(A and B)
Example
A die is rolled. Find the probability of getting an even number or a prime number.
Even = (2,4,6)---n(E)=e
P=(2,3,5)-- n(P)=3
E n P =2--- n(EnP) =1
P(E or P)=p(E)+ 3/6+3/6-1/6 =5/6