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

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”).

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 = .000007 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

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 = .000008

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) = 4 · 3 · 2 52 51 50 = 1/5525 = .0002