banksy wrote:
What is the probability that event E or event F or both will occur?
(1) The probability that event E will occur is 0.6.
(2) The probability that event F will occur is 0.4.
we are asked P(E or F) + P(E and B)
usually, if the two events are mutually exclusive, then:
P(E) + P(F)=1. - and P(E or F)=1, and P(E and F)=0.
if not, then:
P(E or F) = P(E) + P(F) + P(E and F)
and P(E or F)+P(E and F) = P(E) + P(F)
moreover, it might be conditional probability...
1. P(E)=0.6, but we do not know anything about P(F), or about what kind of events these two are. Moreover, we do not know whether there are any relations between these two. not sufficient.
2. P(F)=0.4 - same as 1. so no
at this moment, we crossed A, B, and D. our chances of getting to the right answer increased considerably - probability 50% (see how I used probability even here? :D)
ok, so it might appear that the two events are independent, since P(E)+P(F)=1.
but what if we have a conditional probability?
what if F can be chosen only if E is chosen?
in this case, the probability of getting F is P(E)* # of successes/total outcomes left = 4/10
since we do not know the relationship between these two events, then we cannot give a definite answer.
E