SBM 7B

1
SBM - 7B
Combining Probabilities

• SBM Chapter 7 Probability Living
• with the Odds.

2
IndependentEvents

• From your reading??
• What is the probability of rolling a double 6
  in one roll of two dice?
• P(double 6) P(6) X P(6) 1/6 X
  1/6 1/36

3
And Probability Independent Events

• Two events are independent if the outcome of one
  does not affect the probability of the other
  event.
• Consider two independent events A and B with
  individual probabilities P(A) and P(B). The
  probability that A and B occur together is

P(A and B) P(A) X P(B)
4
And Probability Independent Events (cont)

• This principle can be extended to any number of
  independent events.
• For example, the and probability of three
  independent events A, B, and C is

P(A and B and C) P(A) X P(B) X P(C)
Please Look at Examples 1 2 on pages 419-20
5
DependentEvents

• From your reading??
• Suppose you draw candy randomly from a box of 5
  chocolates and 5 caramels. What is the
  probability of drawing 2 caramels?
• P(2 caramels) P(cara.) X P(cara.)
  5/10 X 4/9
  20/90 2/9

6
And Probability Dependent Events

• Two events are dependent if the outcome of one
  event affects the probability of the other event.
• The probability that dependent events A and B
  occur together is

P(A and B) P(A) X P(B given A)
Where P(B given A) means the probability of
event B given the occurrence of event A
7
And Probability Dependent Events (cont)

• This principle can be extended to any number of
  dependent events.
• For example, the and probability of three
  dependent events A, B, and C is

P(A and B and C) P(A) X P(B given A) X P(C
given A and B)
Please Look at Examples 3 4 on pages 421-22
8
Either/OrProbabilities

• From your reading??
• Suppose we want to know the probability that
  either of 2 events occurs, rather than the
  probability that both events occur.
• We have 2 cases to consider. We call them
• Non-Overlapping Events
• Overlapping Events

9
Either/Or Probability Non-Overlapping Events

• Two events are non-overlapping if they cannot
  occur together.
• If A and B are non-overlapping events, the
  probability that either A or B occurs is

P(A or B) P(A) P(B)
10
Either/Or Probability Non-Overlapping Events
(cont)

• This principle can be extended to any number of
  non-overlapping events.
• For example, the probability that either event A,
  event B, or event C occurs is

P(A or B or C) P(A) P(B) P(C)
11
Either/Or Probability Overlapping Events

• Two events are overlapping if they can occur
  together.
• If A and B are overlapping events, the
  probability that either A or B occurs is

P(A or B) P(A) P(B) - P(A and B)
Please Look at Examples 5 6 on pages 422-24
12
The At Least One Rule (For Independent Events)

• Suppose the probability of an event A occurring
  in 1 trial is P(A). If all trials are
  independent, the probability that event A occurs
  at least once in n trials is

P(at least on event A in n trials) 1 - P(no
events A in n trials) 1 - P(not A in one
trial)n
Please Look at Examples 7 8 on pages 425-26
13
Homework for 7B

• 7B 1 26, 30