We're given the following probabilities:
(a) Yes, 
and 
are mutually exclusive. This is exactly what zero probability of their intersection means. The two events cannot occur simultaneously.
(b) Use the definition of conditional probability to expand:
(c) By the law of total probability,
(d) Bayes' theorem says
If George completed 3/5 of work in 9 days, it means that he needs 3 days to finish 1/5th of the work.
The remaining part is 2/5 because 1-3/5=2/5. 2/5 is also 6/15
From this, how much did George do? in the first 3 days he did 1/5th and then one more day was left, during which he did 1/5/3=1/15th.
So he did in total 1/15+1/5=1/15+3/15=4/15.
this means that Paul did the rest of 6/15, so Paul did 6/15-4/15=2/15.
So we know that he does 2/15 in 4 days, which means that every two days he can do 1/15 of the work
so he would need 15 times 2 days to finish the work - 30 days!
The sum (addition) of -2 and 3 times (3 ·) a number (n)
-2 + 3n
