The professor who sometimes forgets to bring her briefcase to the office, but assume that, each day, the probability that she forgets the briefcase is 1 /8 . Assume that her forgetting is a Bernoulli process.
(1) What is the probability that she remembers to bring her briefcase every day in one week (5 days)?
(2) What is the probability that she forgets to bring her briefcase every day in one week (5 days)?
(3) What is the probability that she forgets to bring her briefcase at least one day in one week (5 days)?
So I'm having a little trouble. The first time I tried this I did the following: 1-(5,0)*1/8^0*7/8^5 Which was incorrect. Any thoughts? Thanks in advance!
$p$ = probability that she forgets to bring the briefcase, then $p = \dfrac{1}{8}$, and $q$ = probability that she remembers to bring the briefcase each day, then $q = 1 - p = \dfrac{7}{8}$. Thus:
a) $P(A) = \left(\dfrac{7}{8}\right)^5$.
b) $P(B) = \left(\dfrac{1}{8}\right)^5$.
c) $P(C) = 1 - \left(\dfrac{7}{8}\right)^5$