Probabilities: + rule

Probabilities: + rule

1. “AND” means MULTIPLY

2. Question?

   • Are both events able to occur at the same time?
     • YES!
       • EG: what is the probability this employee has an advanced degree OR is female?
         • Can choose a women with degree at the same time
           • Use GENERAL + rule
             • P(A or B) = P(A) + P(B) – P(A and B)
             • What is the probability that, in six flips, you get AT LEAST one head?
               • P(at least one 6) = 1 – P(no 6’s)
                 • probability of rolling something other than 6 (“not 6”) is 5/6.
     • NO
       • EG: Throwing a die cannot produce 2 and 6 at the same time
         • If the probability of their simultaneous occurrence is zero
           • it is absolutely impossible to have them both happen at the same time.
             • Two events are disjoint if they are mutually exclusive.
               • “OR” means ADD
                 • P(A or B) = P(A) + P(B)
         • Only can produce 2 OR 6 at the same time
           • Thus, the event to produce 2 or 6 are mutually exclusive
             • If is MUTUALLY EXCLUSIVE, use SPECIAL + rule
               • 1/6+1/6=2/6
     • “A happens” and “A doesn’t happen”
       • either the event happens or it doesn’t happen.
         • With certainty, we can say: one of those two will occur.
           • P(A OR not A) = 1
             • P(A) + P(not A) = 1
               • P(not A) = 1 – P(A)
                 • Complement rule
                   • the probabilistic region in which an event doesn’t occur complements the region in which it does occur.