Question

Suppose that 5 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that all 5 are not black?

Answer 1

Here's the way I see it:  5 cards are drawn, one by one, without replacement.  Half (or 26) of the original deck are black and half (26) are white.

P(5 are not black) = P(5 are red)

P(5 are not black) = P(first card is red) * P(second card is red) * P(third card is red)*P(fourth card is red)*P(fifth card is red) =

(26/52) * (25/51) * (24/50) * (23/49) * (22/48) = 0.025   (answer)

We start with 52 cards.  We draw one, leaving 51 cards, 25 of which are red.  And so on.