# More of David Palay’s Slides. Conditional Probability Given that you had a quiz on Tuesday, what is the Probability that you have homework tonight…

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More of David Palay’s Slides

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

Example:

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

Conditional Probability

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.

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

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}

Method 2: Calculating

TPS Reports

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.

Dependent and Independent events

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?

Tossing two Coins

A useful result!

Even more useful!

But that means…

This works for the probability of more than 2 events!

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

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

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!

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

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

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.

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

One more thing

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