Chapter 7- Probability. A phenomenon is random if any individual outcome is unpredictable, but each outcome tends to occur in a fixed proportion of a very long sequence of repetitions. Examples : Toss a coin Roll a pair of dice Sex of a newborn baby Draw one card from a deck
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Toss a coin
Roll a pair of dice
Sex of a newborn baby
Draw one card from a deck
Winning numbers in a lottery
1. The probability always satisfies 0<P(E)<1
2. The sum of the probabilities of all of the events in a sample space is 1. P(S) = 1
3. For any event E, we have
P(not E) = 1 - P(E)
4. If 2 events A and B have no outcomes in common, then
P(A or B) = P(A) + P (B)
A pizza can be made with any of the following toppings: Cheese, pepperoni, mushrooms, ham, or olives.
in a sample space S are numbers, and that is the probability of the outcome . Then the mean of this probability model is
Random in the sense of showing long-run regularity
By the Law of Large Number guarantees ???