In a deck of cards, let the events A, B, C1, C2, C3 are:

A = the event of picking up a King by random

B= the event of picking up a Spade by random

C1= the event of picking up an Ace

C2= the event of picking up any number card other than the Ace

C3= the event of picking up any picture card

(a). What is P(A), P(B), P(C1), P(C2), P(C3)?

(b) What is P(A|C1), P(A|C2), P(A|C3), P(A\B) , P(A|Bnot )?

(c). Use the total probability theorem to compute P(A)

(d) Use the Bay's theorem to compute P(B|A)