question_answer

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:

(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 aces.

A card of spade or an ace can be drawn in

\[13+4-1=16\] (ways)

Probability of drawing a card of spade or an ace.

\[P=\frac{16}{52}=\frac{4}{13}\]

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

\[P=\frac{8}{52}\]

\[P=\frac{2}{13}\]