Clear Explanation on "PROBABILITY"
Probability is a value between 0 and 1 that a certain event will occur
We can calculate probability by dividing the number of events by the number of possible outcomes
by doing that we can find out the probability for the single event occurring
Example the probability that a fair coin will come up heads is 0.5
mathematically we write:
p(E heads) = 0.5
The act of flipping a coin is called a "trail"
Each trail of flipping a coin can be called an "Experiment"
The sample space is the sum of every possible simple event
Experiments and sample space:
Consider rolling a six-sided die
One roll is an experiment
The simple events are:
E1 = 1 E2 = 2
E3 =3 E4 =4
E5 =5, E6 =6 -----------(Experiments)
therefore, the sample space is :
S={E1,E2,E3,E4,E5,E6}
The probability that a fair die will roll a six:
the simple event is E6 = 6(one event)
total sample space:
S ={E1,E2,E3,E4,E5,E6} (six possible outcomes)
therefore, p(roll six) = 1/6
Ex: A company made a total of 50 trumpet valves, it is determined that one of the values was defective if three valves go into one trumpet, what is the probability that a trumpet has a defective value?
solution :
Calculate the probability of having a defective value:
p(E defective valve) = 1 /50 = 0.02
Calculate the probability of having a defective trumpet
p(E defective trumpet) = 3 x p(E defective valve)
= 3 x 0.02
= 0.06
The probability that a trumpet has a defective valve is 0.06
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