2. Preamble (Past Lesson Brief)
Probability of an event
Mutually ¬ Exclusive Events
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3. Learning Outcomes
By the end of the lesson Students will able to
understand:
Additional rule of probability for mutually & non
mutually events.
Practical implementation of additional rule.
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4. Laws of Probability
Addition Rule 1:
When two events, A and B, are mutually exclusive, the probability that A or B will
occur is the sum of the probability of each event.
P(A or B)=P(AUB) = P(A) + P(B)
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6. Example 2
What is the probability of getting a total of 7 or 11 when a pair of fair dice is
tossed ?
Solution : Let A be the event that 7 occurs and B the event that 11 comes up.
Now, a total of 7 occurs for 6 of the 36 sample points, and a total of 11 occurs
for only 2 of the sample points. Since all sample points are equally likely, we
have P(A) = 1/6 and P(B) = 1/18. The events A and B are mutually exclusive,
since a total of 7 and 11 cannot both occur on the same toss. Therefore,
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8. Addition Rule 2
When two events, A and B, are non-mutually exclusive, there is some overlap
between these events. The probability that A or B will occur is the sum of the
probability of each event, minus the probability of the overlap.
P(A or B) = P(A) + P(B) - P(A and B)
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9. Venn Diagram
Theorem 2.7: If A and B are two non mutually events, then
P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
Additive rule of probability.
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12. Home Assignment
In a high school graduating class of 100 students,54 studied mathematics, 69
studied history, and 35 studied both mathematics and history. If one of these
students is selected at random, find the probability that
(a) the student took mathematics or history;
(b) the student did not take either of these subjects;
(c) the student took history but not mathematics
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13. Home Assignment
A class contains 10 men & 20 women of which half of the men and half of the
women have brown eyes. Find the prob. that a person chosen at random is a man
or has brown eyes.
In a group of 20 adults, 4 out of the 7 women and 2 out of the 13 men wear
glasses. What is the probability that a person chosen at random from the group is
a woman or someone who wear glasses?
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15. References
Probability and Statistics for Engineers and Scientists by Ronald E.
Walpole, Raymond H. Myers, Sharon L. Myers and Keying E. Ye, Pearson;
9th Edition (January 6, 2011). ISBN-10: 0321629116 2
Walpole, P.E., Myers R.H., Myers S.L. (1998), “Probability and Statistics for
Engineers and Scientists”, 7th Ed. Prentice Hall.
Introduction to Statistical Theory Part 1,Prof Sher Muhammad Chaudhry
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