1. Sec. 5-4: Multiplication Rule & Conditional P(x)

2. Multiplication Rule: (“And” p(x)’s)
P(A and B) = P(A) · P(B)
Independent P(x)’s:
When the occurrence of one event does NOT affect the occurrence of another event.
(Items may be “replaced” so p(x)’s are “equally likely”).

3. i.e. Find the probability of pulling a 2♥, 3 ♥, and a 4 ♥ from 3 separate decks.
Find: P(2♥ and 3♥ and 4♥)
P(2♥ and 3♥ and 4♥) = P(2 ♥)·P(3 ♥)·P(4 ♥)
= 1/52 · 1/52 · 1/52 =
i.e. Find P(3 Kings from separate decks)
P(K1 and K2 and K3) = P(K1) · P(K2) ·P(K3)
= 4/52 · 4/52 · 4/52
= .0005

4. Dependent P(x)’s: P(B|A)
One event DOES alter the p(x) of another event.
(Items are NOT replaced so P(x)’s change)
i.e. Let’s NOT put the cards back from the previous examples.
P(2♥ and 3♥ and 4♥)
= P(2 ♥)·P(3 ♥|2 ♥)·P(4 ♥| 2 ♥,3 ♥)
= 1/52 · 1/51 · 1/50 =

5. i.e. Find the p(x) of pulling 3 kings without replacing the cards.
P(K1 and K2 and K3)
= P(K1) · P(K2|K1) · P(K3|K1&2)
= · ·
= 1/5525 = .0002