A card is drawn form a pack of 52 cards so that each card is equally likely to be selected. In which of the following cases are the events A and N independent?
i. A=the card drawn is a king or queen, B=the card drawn is a queen or jack
ii. A=the card drawn is black, B=the card drawn is a king
iii. B=the card drawn is a spade, B=the card drawn in an ace
(i) In a pack of 52 cards there are 4 king,4 queen,4 jack
A=the card drawn is a king or queen
B=the card drawn is a queen or jack
A∩B=Card is a queen
Therefore A and B are not independent events
(ii) In a pack of 52 cards there are 4 king,26 black
A=the card drawn is a black
B=the card drawn is a king
A∩B=Card is a black king
Therefore A and B are independent events
(iii) In a pack of 52 cards there are 13 spade,4 ace
A=the card drawn is a spade
B=the card drawn is an ace
A∩B=Card is an ace from spade
Therefore A and B are independent events