An ordinary deck of 52 cards of four suits. The queen of spades is randomly drawn...

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An ordinary deck of 52 cards of four suits. The queen of spades is randomly drawn...

An ordinary deck of 52 cards of four suits. The queen of spades is randomly drawn and removed from the well shuffled deck. What is the conditional probability p that one card drawn randomly from the remaining deck will be a face card or a club?

math Statistics-And-Probability

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Answer 1

Answer #1

Number of suits =4

Number of face cards(Jack, Queen, king ) in each suit = 3

Number of face cards in standard deck = 4 x3=12

A: Event of drawing queen of spades (first card)

B : Event of drawing a face card or a club(second card)

The queen of spades is randomly drawn and removed from the well shuffled deck.

p : Conditional probability hat one card drawn randomly from the remaining deck will be a face card or a club given that the queen of spades is randomly drawn and removed from the well shuffled deck = P(B|A)

Given that first card drawn is queen of spades and removed

Queen of spades is face card

Number of cards left in the deck = 52-1 =51

Number of face cards left in the deck = 12-1 = 11

Number of club cards left in the deck = 13

Number of club and face cards left in the deck = 3 (Club jack, Club queen, club king)

Probability of drawing a face card or club card = Probability of drawing a face card + Probability of drawing a club card - Probability of drawing club face card

Probability of drawing a face card = Number of face cards left in the deck / Number of cards left in the deck =11/51

Probability of drawing a club card = Number of club cards left in the deck / Number of cards left in the deck =13/51

Probability of drawing a club card - Probability of drawing club face card = Number of club and face cards left in the deck / Number of cards left in the deck = 3/51

Probability of drawing a face card or club card = Probability of drawing a face card + Probability of drawing a club card - Probability of drawing club face card = 11/51 + 13/ 51 - 3/51 = 21/51

p : Conditional probability hat one card drawn randomly from the remaining deck will be a face card or a club given that the queen of spades is randomly drawn and removed from the well shuffled deck = 21/51 = 7/17

p : Conditional probability hat one card drawn randomly from the remaining deck will be a face card or a club given that the queen of spades is randomly drawn and removed from the well shuffled deck = 7/17 = 0.411765

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Answer 2

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