Cards are drawn at random from an ordinary deck of 52 cards, one by one and without replacement. We are interested in the probability that no heart is drawn before the ace of spaces is drawn.
a) What is the probability of drawing the ace of spades in the first draw ?
b) What is the probability of not drawing the ace of spades nor any heart in the first draw?
c) What is the probability of not drawing the ace of spades nor any heart in the first draw, and drawing the ace of spades in the second draw?
d) What is the probability of not drawing the ace of spades nor any heart in the first d-1 draws, and drawing the ace of spades in the d-th draw, d = 2,..., ?
e) Use a through d to deduce an expression for the probability we are eventually interested in .