My course says that if you draw two cards from a deck, define the events: S1 = ‘first card is a spade’ and S2 = ‘second card is a spade’ then P(S2)=13/52. Why 13/52? My thinking is this:
P(S2) is the probability that the second card is a spade given that we do not know whether the first card is a spade or not. If the first card is a spade then the chance that the second card is a spade is 12/51. If the first card is not a spade then the chance is 13/51. So we have a 13/52 chance that P(S2) is 12/51 and we have a 39/52 chance that P(S2) is 13/51. How can you say P(S2)=13/52?