Hey guys, this is Irish and today we learned about the “Probability of Independent and dependent events”.

Mutually Exclusive events are where events can not both occur at the same time. (The probability of drawing a king or a queen when a single card is drawn from a deck of cards – the card can not be king and queen at the same time).

• Probability for mutually exclusive events: P(E or F) = P(E) + P(F)
• Probability for non-mutually exclusive events: P(E or F) = P(E) + P(F) – P(E and F)
  

Complementary events are when one event occurs if and only if the other doesn’t.

• Complementary events: P(E) + P(F) = 1
  

Independent Events are when two events occur but do not influence the outcome of each other.

• Probability of Independent Events: P(E and F) = P(E) • P(F)
  

NOTE: DON’T REDUCE UNLESS OTHERWISE STATED

Example #1: Two cards are drawn from a desk of 52 cards. Find the probability that they are both face cards if the first card is…

a) replaced?
PFACE CARD (#1) = 12/52
PFACE CARD (#2) = 12/52
PBOTH FACE CARD = 12/52 • 12/52 → 9/169


b) not replaced?
PFACE CARD (#1) = 12/52
PFACE CARD (#2) = 11/51
PBOTH FACE CARD = 12/52 • 11/51 → 11/221

Example #2: A box contains 5 chocolate candies, 3 cherry candies and 7 caramel candies…

a) if one candy is chosen, what is the probability it will be cherry or caramel?
PCHERRY = 3/15
PCARAMEL = 7/15
PCHERRY and CARAMEL = 3/15 + 7/15 → 10/15

b) if two candies are drawn what is the probability that both are chocolate or both cherry? (without replacement).

PCHOCOLATE (#1) = 5/15
PCHOCOLATE (#2) = 4/14
PBOTH CHOCOLATE = 5/15 • 4/14 → 20/210

PCHERRY (#1) = 3/15
PCHERRY (#2) = 2/14
PBOTH CHERRY = 3/15 • 2/14 → 6/210
PCHOCOLATE and CHERRY = 20/210 + 6/210 → 26/210