Hello, MaOp91!

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 oflocations,eight

. .

(b) The opposite of "at least one B" is "no B's" (all R's).

Therefore: .

(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

Find: .

From DeMorgan's Law: .

Therefore: .