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More of David Palay’s Slides

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Conditional Probability Given that you had a quiz on Tuesday, what is the Probability that you have homework tonight…

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Example:

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This is the probability of the employee’s TPS report having the wrong coversheet, GIVEN that the employee is male.

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Conditional Probability

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Our Company There are 15 people in the small company. 9 are male 5 females filed improper TPS reports 8 employees filed improper TPS reports. From this, we can figure out the probability of having an improper TPS report given that the employee is male.

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Method 1 Create a table: Use table to calculate probability MaleFemaleTotal Proper TPS Improper TPS Total

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Example When rolling 2d6, what is the probability that the sum is a 7, GIVEN THAT ONE OF THE DICE IS A 1. {1,1} {1,2} {1,3} {1,4} {1,5} {1,6} {2,1} {2,2} {2,3} {2,4} {2,5} {2,6} {3,1} {3,2} {3,3} {3,4} {3,5} {3,6} {4,1} {4,2} {4,3} {4,4} {4,5} {4,6} {5,1} {5,2} {5,3} {5,4} {5,5} {5,6} {6,1} {6,2} {6,3} {6,4} {6,5} {6,6}

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Method 2: Calculating

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TPS Reports

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Dependent and Independent events Dependent events – 2 events where the outcome of one is influenced by the outcome of the other. Independent events – 2 events who’s outcomes are completely unchanged based on the outcomes of each other.

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Dependent and Independent events

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Tossing two Coins If A is getting heads on the first toss, and If B is getting heads on the second toss, Are A and B dependent or independent?

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Tossing two Coins

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A useful result!

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Even more useful!

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But that means…

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This works for the probability of more than 2 events!

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Ok, take a second…. Breath… We just covered a lot with very little explanation. So, we’re going to do some examples.

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Dependent vs. Independent Determine whether the events are independent or dependent 1)A: a coin comes up heads B: 1d6 comes up even 2)A: 1d6 is thrown and comes up even B: a second d6 is thrown and the sum of the two is greater than 4 3)A: An ace is drawn from a standard deck of cards B: A second ace is drawn from the same deck

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Uh-oh…. Wait a sec. A: An ace is drawn from a standard deck of cards B: A second ace is drawn from the same deck We can come up with two different answers. It depends on if we put the first card BACK or NOT!

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Replacement We talked about it with combinations & permutations, and now we need to incorporate it into independent & dependent events.

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Replacement Namely, if we have replacement, does it make it dependent or independent? Take our deck of cards example. A: An ace is drawn from a standard deck of cards B: A second ace is drawn from the same deck

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Replacement If we put the first card back into the deck (and re-shuffle) then we have an independent event. The first card has no impact on what the second card could be.

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Replacement Alternatively, if we leave the first card out, then the probabilities for the second card have changed.

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One more thing

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Probability Distributions and Expected Value

Probability Distributions and Expected Value

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