chapter 15 probability rules! - yorktown · 15(1).notebook 2 november 21, 2011 the probability for...
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Chapter 15 Probability Rules!
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The probability for any event, A, that is made of equally likely outcomes is:
When working with probabilities, make a picture (Venn diagram or tree diagram or contingency table). This helps you think through probabilities of compound and overlapping events.
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General Addition Rule
Probability that A or B or both occur:
P(A∪B) = P(A) + P(B) - P(A∩B)
If A and B are disjoint:P(A∪B) = P(A) + P(B)
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Conditional Probability P(B|A) is pronounced "the probability of B given A".
We look at the outcomes of A and find in what fraction of those outcomes B also occurred.
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General Multiplication Rule
P(A∩B) = P(A) x P(B|A) or P(B) x P(A|B)
Events A and B are independent whenever P(B|A) = P(B)
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Drawing without Replacement
The probability of drawing a red card from a deck of fullyshuffled cards is 26/52. If a red card is drawn and not replaced, then the probability of drawing another red card is 25/51.
We often sample without replacement. If we draw from a very large population, the change in the denominator is too small to worry about. But when there's a small population (like a deck of cards), we need to adjust the probabilities.
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Tree Diagrams are displays of conditional probabilities and show sequences of events as paths that look like branches of a tree.
37. Absenteeism. A company's records indicate that on any given day about 1% of their day shift employees and 2% of the night shift employees will miss work. Sixty percent of the employees work the day shift. What percent of employees are absent on any given day?
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Reversing the Conditioning
We have P(A|B) but want to reverse the probability P(B|A). We need to find P(A∩B) and P(A). A tree is often a convenient way of finding these probabilities.
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Hw p.339; 21,40 p.361;4,20,21,23,29,34,36,43 ANS
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