Statistics

Statistics

4.3 Probability

There are a few rules for probability:

1. Probabilities can be represented with classical formulas

2. P always stands for probability

3. The range for probability is always 0 (not occurring) to 1 (occurs)

4. You will always have at least two events: A and/or B

• The probability of event A only occurring or not occurring is written as: o P (A) = [0, 1]. • The probability that event A will not occur is written as: o P(A B ) = 1 – P(A) ▪ This is the same as calculating the probability of B • The probability of A or B occurring is written as: o P (A ∪ B) = P(A) + P(B) – P(A ∩ B) o Or for mutually exclusive: P(A ∪ B) = P(A) + P(B) ▪

The symbol ∪ stands for union and that the events are A or B or both ▪ The symbol ∩ stands for intersect and states that A and B have events in common

• The probability that A and B will occur is written as: o P(A ∩ B) = P(AIB) * P(B) = P(BIA) * P(A)

o Or if the events are independent: P(A ∩ B) = P(A) * P(B) ▪ The symbol I means to include

• The probability of A occurring given B is written as: o P(AIB) = P(A∩ B) / P(B)

Application of Probability

Probabilities are used to predict outcomes and they have many different applications. Probabilities can be used to predict:

• Economic predictions and outcomes • Consumer reaction to a new product • Scientific research • Future business forecast • Voting trends

*Can you think of more ways probabilities are used in everyday life?

© 2015

Achieve

Page 36 of 94