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 \[P=\frac{8}{52}\] \[P=\frac{2}{13}\]
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