probability – the briefest possible review.

• P(event A) = relative frequency of Event A / large number of events (where A is possible)
• Conditional Probability = p(a) given that b has already happened.  P(a|b)
• independent events: event b has absolutely no effect on P(a).  P(a)= (a|b)
  • if a and b are independent, P(A & B) = P(B)P(A)
• dependent events : P(a) is not the same as P(a|b)
• mutually exclusive events : if b occurs a cannot (and vice versa)  P(a|b) = 0.  
• if A & B are mutually exclusive then P(A or B) = P(a) +P(b).