Question

A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is
(i) A card of spade or an ace
(ii) A black king
(iii) Neither a jack nor a king
(iv) Either a king or a queen

Answer 1

(i) Let S be the sample space of drawing a card from a well-shuffled deck

Then, S=52

There are 13 spade cards and 4 aces in a deck.

As a ace of spade is included in 13 spade cards,So there are 13 spade cards and 3 other aces.

A card of spade or an ace can drawn in 13+4-1=16 (ways)

Probability of drawing a card of spade or an ace.

P=$\frac{16}{52}$

P =$\frac{4}{13}$

(ii)There are 2 black king cards in a deck.

Probability of drawing a black king

P=$\frac{2}{52}$

P=$\frac{1}{26}$

(iii) There are 4 jack and 4 king cards in a deck.

So,there are 52-8=44 cards which are neither jack nor king

Probability of drawing a card which is neither a jack nor a king

P=$\frac{44}{52}$

P=$\frac{11}{13}$

(iv) There are 4 queen and 4 king cards in a deck

So,there are 8 cards which are either king or a queen.

Probability of drawing a card which is either king or a queen

P=$\frac{8}{52}$

P=$\frac{2}{13}$