© Jill Zarestky
Math 141 Week in Review
Week in Review 7 Key Topics
7.4 Use of Counting Techniques in Probability
Let S be a uniform sample space and E be any event in S. Then
n(E)
number of outcomes in event E
P (E) =
=
number of outcomes in the sample space S n ( S )
•
•
Use permutations and combinations to find the numbers of outcomes.
The rules of probability still apply:
o If E and F are mutually exclusive, P(E ∪ F) = P(E) + P(F)
o If E and F are any two events, P(E ∪ F) = P(E) + P(F) – P(E ∩ F)
o P(EC) = 1 – P(E)
7.5 Conditional Probability and Independent Events
Conditional Probability
• If E and F are events of an experiment such that P(E) ≠ 0, then the conditional probability
P (E ! F)
that event F will occur given that event E has occurred is: P ( F | E ) =
P (E)
•
Rearrange to get the product rule: P(E ! F ) = P(E )P(F | E )
•
Use tree diagrams to visually represent situations.
Independent Events
• Two events are independent if the outcome of one does not affect the outcome of the
other.
• Events E and F are independent if P ( E ! F ) = P ( E ) " P ( F ) .
o Use this as your “test.”
• If E and F are independent then P ( E | F ) = P ( E ) and P ( F | E ) = P ( F ) .
7.6 Bayes’ Theorem
Bayes’ Theorem
•
•
P (E) P (F | E)
P (F)
Use this to “switch the givens.”
P (E | F) =
1