Download Sec. 6.3 Part 2 Blank Notes

Section 6.3 Part 2
Extended Multiplication Rules
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Recall that the union of a collection of events is the event that any of them occur.
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The intersection of any collection of events is the event that all of the events occur.
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To extend the multiplication rule to the probability that all of several events occur, the key is to condition each
event on the occurrence of all of the preceding events.
𝑃(𝐴 and 𝐵 and 𝐶) = 𝑃(𝐴) × 𝑃(𝐵|𝐴) × 𝑃(𝐶|𝐴 and 𝐵)

See example 6.22 on p.372
Tree Diagrams Revisited
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Probability problems often require us to combine several of the basic rules into a more elaborate calculation.
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Each segment in the tree is _________________________________. Each branch shows a path that must be
taken to ___________________________________
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The probability written on each segment is the conditional probability that that segment is given after reaching
that point from each branch.

See example 6.23 on p.373

The tree diagrams combine the addition and multiplication rules:
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The multiplication rule says that the probability of reaching the end of any complete branch is the
product of the probabilities written on its segments.

The probability of ____________________________ is then found by __________________________of
all branches that are part of ________________
Independence


The conditional probability _____________ is generally _______________ the unconditional probability _____

That is because the occurrence of event A generally gives us some additional information about whether
or not event B occurs.
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If knowing that A occurs __________________ about B, then ___________________________
The formal definition states:

Two events A and B that both have positive probability are independent if:
𝑃(𝐵|𝐴) = P(B)

We now see that the multiplication rule for independent events ____________________________, is a special
case of the general multiplication rule, _____________________________________

See example 6.25 on p.376