From a well-shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is :
(i) a face card
(ii) not a face card
(iii) a queen of black colour
(iv) a card with number 5 or 6
(v) a card with number less than 8
(vi) a card with number between 2 and 9

Question

From a well-shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is :
(i) a face card
(ii) not a face card
(iii) a queen of black colour
(iv) a card with number 5 or 6
(v) a card with number less than 8
(vi) a card with number between 2 and 9

KnowledgeBoat · Accepted Answer

There are 52 cards in a deck. We have, the total number of possible outcomes = 52 (i) No. of face cards in a deck of 52 cards = 12 (4 kings, 4 queens and 4 jacks) ∴ No. of favourable outcomes = 12 P(drawing a face card) = . Hence, probability of drawing a face card = . (ii) As, probability of drawing a face card and a non-face card are complimentary event. ∴ Probability of drawing a face card + Probability of drawing a non-face card = 1 ⇒ Probability of not drawing a face card = 1 - Probability of drawing a face card ⇒ Probability of not drawing a face card = . Hence, probability of not drawing a face card = . (iii) There are 2 queens of black colour (1 of each club and spade). ∴ No. of favourable outcomes = 2 P(drawing a queen of black colour) = . Hence, probability of drawing a queen of black colour = . (iv) There are 4 cards (1 of each suit) of each 5 and 6 number. ∴ No. of favourable outcomes = 8 P(drawing a card with number 5 or 6) = . Hence, probability of drawing a card with number 5 or 6 = . (v) There are {2, 3, 4, 5, 6, 7} numbered cards of each heart, diamond, club and spades. ∴ No. of favourable outcomes = 6 × 4 = 24. P(getting a card with number less than 8) = . Hence, the probability of drawing a card with number less than 8 = . (vi) There are {3, 4, 5, 6, 7, 8} numbered cards of each heart, diamond, club and spades. ∴ No. of favourable outcomes = 6 × 4 = 24. P(getting a card with number between 2 and 9) = . Hence, the probability of drawing a card with number between 2 and 9 = .

Mathematics

From a well-shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is :
(i) a face card
(ii) not a face card
(iii) a queen of black colour
(iv) a card with number 5 or 6
(v) a card with number less than 8
(vi) a card with number between 2 and 9

Probability

Related Questions

In a match between A and B;
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A and B are friends. Ignoring the leap year, find the probability that both friends will have:
(i) different birthdays?
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Mathematics

From a well-shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is :(i) a face card(ii) not a face card(iii) a queen of black colour(iv) a card with number 5 or 6(v) a card with number less than 8(vi) a card with number between 2 and 9

Probability

Related Questions

In a match between A and B;(i) the probability of winning of A is 0.83. What is the probability of winning of B?(ii) the probability of losing the match is 0.49 for B. What is the probability of winning of A?

A and B are friends. Ignoring the leap year, find the probability that both friends will have:(i) different birthdays?(ii) the same birthday?

From a well-shuffled deck of 52 cards, one card is drawn. Find the probability that the card drawn is :
(i) a face card
(ii) not a face card
(iii) a queen of black colour
(iv) a card with number 5 or 6
(v) a card with number less than 8
(vi) a card with number between 2 and 9

In a match between A and B;
(i) the probability of winning of A is 0.83. What is the probability of winning of B?
(ii) the probability of losing the match is 0.49 for B. What is the probability of winning of A?

A and B are friends. Ignoring the leap year, find the probability that both friends will have:
(i) different birthdays?
(ii) the same birthday?