Estimating Probability

Experimental Estimating of Probability

 You can describe probabilities that are estimated by:

Estimated P(U) = n(U) ⁄ n(T)

Theoretical Estimation of Probability
Sometimes you can easily see the probability, for example, tossing a coin.

P(H) = 1 ⁄ 2



You have to make sure that you can assume that each option are equally likely. But expressed formally, the P(A) is:

P(A) = n(A) ⁄ n(Ɛ)


Where P(A) is the probability that the event occurs, n(A) is the number of ways that A can occur and n(Ɛ) is the total number of ways all of the different events can occur.

Probabilities of 0 and 1
Probability can be from certainty to impossibility. Here's a couple of examples of the two extremes:
• Rolling a single die
- It's certain that the result will be in the range of 1 and 6 inclusive.
- It's impossible that the result is 7.

• Tossing a coin
- It's certain that the result will either heads or tails.
- It's impossible that the result will neither be heads or tails.

Certainty
The expression that the probability of an event is certain is:

n(A) ⁄ n(Ɛ) = 1


Impossibility
The expression that the probability of an event is impossible is:

n(A) ⁄ n(Ɛ) = 0 ⁄ n(Ɛ) = 0


P(A) is more than or equal to 0 (impossible) and less than or equal to 1. So, 0 ≤ P(A) ≥ 1.

The Complement of An Event
The complement of an event, A is denoted by A'. This is the event that A doesn't happen, i.e. "not-A". We can find the complement by taking A from 1.

Example: If out of 50 matches, 45 didn't light, what was the probability that a randomly selected match would not have lit?
The probability that a randomly selected match lit is:
P(A) = 45 ⁄ 50 = 0.9
P(A') = 1 - P(A)
P(A') = 1 - 0.9
P(A') = 0.1

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