Mathematics

Problem

A card is drawn at random from a well-shuffled pack of 52 playing cards, replaced, the pack is shuffled again, and then a second card is drawn. Let

A

: “the first card drawn is a King”,

B

: “the second card drawn is a heart”. a. (i) Calculate

P(A)

P(B)

and

P(A \cap B)

. b. (ii) Test whether the events

A

and

B

are independent, giving complete working. c. (iii) Without repeating the calculations, determine whether the events

A

and

B

would remain independent if the first card were not replaced before drawing the second. Justify your conclusion.