Events and their complements - rFronteddu/general_wiki GitHub Wiki

• $A^c$ is everything that A is not.
• => A + $A^c$ is the sample space
• Since P(A) + P(B) + ... = 1 -> P(A) = 1-P($A^c$)

Example: coin toss

• P(Head) = 1 - P(Tail)

Note:

• If the sum of all outcomes is > 1 ⇒ we must be double-counting outcomes
• If the sum of all outcomes is < 1 ⇒ we must be missing some outcomes

Example: coin toss

• if A = roll 1 or 2 or 3 or 4 or 5 → P(A) = 5/6 = P(not roll 5) = 1 - 1/6 = 5/6