From a deck of 52 cards, ace, king, queen and jack of black suits are removed. From the remaining well shuffled cards, one card is drawn at random. Find the following probabilities regarding the drawn card:
(1) It is a face card.
(2) It is a card of a red suit.
(3) It is a card of a black suit.
Answers
Answer:
(1)
3/22
(2)
13/22
(3)
9/22
Step-by-step explanation:
hope this helps you⟵(O_O)
If from a deck of 52 cards, ace, king, queen and jack of black suits are removed and from the remaining well shuffled cards, one card is drawn at random, the probability that the drawn card is
a face card = 3/22
a card of a red suit = 13/22
a card of a black suit = 9/22
Given:
i) A deck of 52 cards
ii) Ace, king, queen and jack of black suits are removed from this deck
To find:
Probability that a randomly drawn card from this remaining well shuffled cards is a
(1) face card
(2) card of a red suit
(3) card of a black suit
Solution:
The formula for probability is
Probability of an even happening P(E) =
Number of favourable outcomes/Total no of outcomes
Since ace, king, queen and jack of black suits are removed from the deck consisting of 52 cards,
Total no. of cards removed = 4 cards of clubs + 4 cards of spades
= 8
Total no. of remaining cards = 52 - 8
= 44
(1)
Face card in a deck of cards are kings, queens, and jacks
Face cards of clubs and spades have been removed
=> Total number of face cards in this deck
= 3 face cards of hearts + 3 face cards of diamonds
= 6
Probability of a face card = 6/44
= 3/22
(2)
Total number of cards of red suits in this deck
= 13 cards of hearts + 13 cards of diamonds
= 26
Probability of a card of a red suit = 26/44
= 13/22
(3)
Total number of cards of black suits in this deck
= 9 cards of spades + 9 cards of clubs
= 18
Probability of a card of a red suit = 18/44
= 9/22
Hence,
P(face card) = 3/22
P(card of a red suit) = 13/22
P(card of a black suit) = 9/22
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