Question

Two cards are successively dealt from a deck of 52 cards. Let A be the event “the first card is a king” and B be event “the second card is a ace.” Are these two events independent?

Answer 1

here as second card ace probability depends on wheater first card is ace or not ;therefore above events are not indepednent,

above can be proved numerically as follows:

here P(first card is king)=P(A)=4/52=1/13 (as there are 4 king out of 52 cards)

P(B)=P(second card is ace)=P(fist card ace and second ace)+P(first not ace and second ace)

=(4/52)*(3/51)+(48/52)*(4/51)=4/52=1/13

P(A n B)=P(first card is king and second is ace)=(4/52)*(3/51)=1/221

as P(A n B) is not equal to P(A)*P(B) ; therefore A and B are not independent.