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
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 = .
Answered By
Related Questions
Face cards of spades are remove from the pack of 52 cards and the remaining cards are well shuffled. Then a card is drawn from the pack.
Statement (1): The probability of drawing a face card is .
Statement (2): Kings, queens and jacks are the three face card and so the total number of face cards in the pack of 52 card is 3 x 4 = 12.
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
In a lottery ticket, there are 20 prizes and 25 blanks.
Statement (1): Probability of not getting the prize = 1 -
Statement (2): P(getting prize) + P(blank) = 1
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
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?