Statistics for Decision- Making in Business - Maricopa Community ...

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Conditional probability is quite useful when used in the correct way. The counterintuitive problem below will allow us to shed light on how important it really is to think about dependencies. Example 7: As part of a narcotics checkpoint, officers randomly search freight trucks for shipments of illegal drugs. The officers search a small number of crates in the trucks that are chosen for random inspection. Suppose that, unbeknownst to the officers, there are two trucks ahead, one of which contains one crate with illegal drugs. This truck has a total of 8 crates, while the truck without drugs has a total of 5 crates. One of the two trucks will be randomly chosen. What is the probability that the officers find the drugs SOLUTION: At first, it is tempting to say that the probability is , however this is not accurate. The probability that the officers find the crate with drugs is dependent on them choosing the correct truck first! Let Two things must happen: they must choose the correct truck and they must choose the correct crate. Randomly choosing one of the two trucks is equiprobable, ( ) . If the correct truck is chosen, then the probability of choosing the correct crate is , that is, ( ) ( ) ( ) ( ) Why is it not valid to say 1/13 It might appear that probability is simply pulling a “fast one” on our intuition. A simple way to think about it is as follows: there is not just one random process here. If all the crates were in the same truck, there would indeed be a 1/13 chance that we‟d get the right crate. However, there are two random processes here. If you don‟t choose the correct truck, then choosing the correct crate is impossible. The likelihood of the second random process leading to the correct crate is indeed deeply affected by the outcome of the first random process! Example 8: Reconsider Example 7:: Let‟s say that the second truck had two crates with shipments of drugs. As before, one of the two trucks will be randomly chosen. What is the probability that the officers find the drugs SOLUTION: Statistics for Decision-Making in Business © Milos Podmanik Page 114
This can happen in one of two ways: the truck with 8 crates ( ) is selected and the one correct crate is chosen OR the truck with 5 crates ( ) is selected and one of the two correct crates is chosen We will first create a small tree diagram showing the possible outcomes. The beauty of this diagram is that it displays the conditional probabilities on the right “stems” of the tree for each initial choosing of the truck. The probability that drugs are found would thus be: Truck 1: Truck 2: Since these are distinct outcomes and cannot both occur (there is no overlap in the events), it is okay to add them Thus, there is a 37% chance that drugs are found between the two trucks. Again, note that the probability is not simply , as our intuition might falsely lead us to believe. To formalize the tree above, Let Statistics for Decision-Making in Business © Milos Podmanik Page 115
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Statistics for Decision- Making in
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A Note to Students This book is far
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6.3 Confidence Interval for ̂ 202
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of transporting such an animal. Not
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Account Type Revenue ($) New $5,296
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For the present time, we‟ll proce
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Row Labels Average of Revenue ($) M
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(SOURCE: Essentials of Modern Busin
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1.3Statistics in Excel When conduct
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We can make it a bit more presentab
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For measures such as the range, Exc
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We get: We can do the same for Old.
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Chapter 2 Visual Representations of
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We now have to enter a formula for
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We know from the data that this val
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Alternatively, it is possible to in
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Selected the copied graph. In Chart
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2. The following data represents pe
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Frequency 2.2 Visualizing Quantitat
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You can either choose to have Excel
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If we had additional variables, the
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Select PivotChart and select the fi
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Frequency To make solid black lines
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Relative Frequency Histogram of Cal
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a. Using Excel, find the mean and r
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2.3.2 Percentile Another useful too
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2.3.4 Rank What if, on the other ha
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Page 71 and 72: This gives us a nice measure of how
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Page 75 and 76: Lastly, a normal curve is the most
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Page 81 and 82: Chapter 3 Probability and Decision
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Page 89 and 90: 3.2 Joint Probability In the previo
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Page 93 and 94: There is less than a 1% chance that
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Page 99 and 100: 3.3 Probability of Unions Imagine t
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Page 105 and 106: Homework Problems - 3.3 1. A gaming
Page 107 and 108: 3.4 Conditional Probability In many
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Page 111 and 112: We could just as well have written,
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Page 121 and 122: 1 st Bushel 2 nd Bushel U1 U1 U2 U2
Page 123 and 124: Which, in its final state gives: Th
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Page 139 and 140: Where The expected value is: , - (
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Page 147 and 148: For men, we see that the most frequ
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Page 151 and 152: Example 1: A fair-two sided coin is
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Density Resulting in a standard dev
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Density Without going into detail h
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a. What is the probability that the
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Statistics for Decision-Making in B
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As you can see, this is a difficult
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We wish to know the area of the sha
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We can easily find that the probabi
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In the second section, we can check
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Chapter 6 Sampling Distributions an
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Thus, the standard deviation would
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The Central Limit Theorem (CLT) has
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can set this up in our applet by ha
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3) We cannot use this sample to cal
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Thus, we need to find the lower and
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DULY CAUTIONED: The assumptions her
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Homework Problems -6.2 1. In a samp
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Hypothesis Test Conclusion Test Say
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Hypothesis Test Conclusion Since yo
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SOLUTION: d. A generic conclusion s
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1.2 Descriptive VS. Inferential Sta
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Relative Frequency 35% 30% 25% 20%
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Repair Cost Mean 971 Standard Error
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Probability Pizza Size Distribution
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