Calculating Probability
By DarthVader
Date: 2022-05-16
Topic: 113 see comments
Post views: 1170
Calculating Probability
In standard mathematical notation, the probability of a particular event A happening is expressed as:
P(A) ∈ [1, 0]
Where ∈ [1, 0] means that the value of P lies in the range 0 to 1. So the probability of tossing a coin that lands showing ‘tails’ would be written as P(T) = 0.5 or 50%
Probability Of Two Independent Events Occurring At The Same Time
overall probability of independent events occurring = probability of the first event × probability of the second event
Using standard probability notation:
P(A ∩ B) = P(A) × P(B)
Where the symbol ∩ means ‘AND’.
This expression can be read as ‘the probability of A and B occurring is equal to the probability of A occurring multiplied by the probability of B occurring’.
Probability Of At Least One Event Occurring
Probability = Probability of A occurring + Probability of B occurring − Probability of both occurring
In probability notation:
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
∪ - denotes ‘OR’
Example:
The valve on an oil storage tank has a 1 in 10,000 chance of failing each time the tank is filled. If the tank is filled each day, how often is failure likely?
The only way to answer this question is to calculate the probability of failure in a given time interval.
The calculation that the tank doesn't fail on any occasion is given by 1 minus the probability that it does fail:
1 − 1/10000 = 0.9999
This is the probability of failure on one occasion, for the probability of failure on two occasions, raise the probability for one occasion to the power of 2:
0.99992
Then for the probability of failure on three occasions raise it to the power of 3.
To calculate the probability of failure over 25 years, you need to multiply 25 by the number of days:
25 × 365 = 9000 (to 1 s.f)
So the probability of failure is:
0.99999000 = 0.4066 = 41%
This means that the probability of non-failure is: 59%
| Comments | Creator | Date | ID |
|---|
