Let E and F be two mutually exclusive events and suppose P(E) = 0.4 and P(F) = 0.2. Compute the probabilities below.
Draw the Venn diagram. Since E and F are mutually exclusive, they
do not overlap. The rectangle represents the entire sample space,
which has probability 1. Therefore the region outside the regions E
and F must have probability 0.4, so that all three regions will have
probability 1, which means that all three probabilities must total 1.
(a) P(E intersection F).That's the probability of where the circle
overlap. Since they do not overlap, the probability is 0.
(b) P(E union F).That's the probability of being in either of the
two circles, which is 0.4+0.2 = 0.6
(c) P(Ec).That's the probability of not being inside the left circle, which is either
gotten by 1-0.4 = 0.6 or by adding the two probabilities
not including the left circle which is 0.4+0.2 = 0.6
(d) P(Ec intersection Fc).That's the probability of not being in E and not being in F, which means being
outside both circles. So the probability is 0.4.
Edwin
