Q. 34.3( 3 Votes )

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

Answer :

(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



AB=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



AB=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



AB=Card is an ace from spade





Therefore A and B are independent events


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