Probability A and B

• P(A) + P(A’) = 1
• P(AUB) = P(A or B) = A union B
• P(A?B) = P(A and B) = A intersect B
• P(AUB) = P(A) + P(B) – P(A?B)
• P(AUB) = P(A) + P(B)  for mutually exclusive events

Probability A and B and C

• For 3 sets A, B, and C:
  P(AuBuC) = P(A) + P(B) + P(C) – P(AnB) – P(AnC) – P(BnC) + P(AnBnC)
• No. of persons in exactly one set: 
  P(A) + P(B) + P(C) – 2P(AnB) – 2P(AnC) – 2P(BnC) + 3P(AnBnC)
• No. of persons in exactly two of the sets: P(AnB) + P(AnC) + P(BnC) – 3P(AnBnC)
• No. of persons in exactly three of the sets: P(AnBnC)
• No. of persons in two or more sets: P(AnB) + P(AnC) + P(BnC) – 2P(AnBnC) 
• No. of persons in at least one set: P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + 2 P(AnBnC)