Since the discs are replaced: .1. A box contains 35 red discs and 5 black discs.
A disc is selected at random and its colour noted.
The disc is then replaced in the box.
(a) In eight such selections, what is the probability that a black disc is selected:
. . (i) exactly once?
. . (ii) at least once?
(a) We can solve this without the Binomial Theorem.
Suppose the outcome is: . in that order.
. . Then the probability is: .
Since the one can appear in any of eight locations,
(b) The opposite of "at least one B" is "no B's" (all R's).
(b) The process of selecting and replacing is carried out 400 times.
What is the expected number of black discs that would be drawn?
Since , we would expect get a black disc: . times.
2. For the events and
From DeMorgan's Law: .