Two cards are drawn without replacement from a well-shuffled deck of 36 playing
ID: 3293527 • Letter: T
Question
Two cards are drawn without replacement from a well-shuffled deck of 36 playing cards. What is the probability that the second card drawn is a spade given that the first card drawn was not a spade? What is the probability that the second card drawn is a spade given that the first card drawn was a spade? A)1/12, 12/25 B) 5/6, 43/44 C) 5/11, 1/43 D) 9/35, 8/35 I know how many spades are in a regular deck=13 ANONYMOUS SAID I NEED TO KNOW SPADES IN A NORMAL 52 CARD DECK IT IS 13 BUT THAT IS NOT HELPFUL
Explanation / Answer
A deck of cards has 4 suits, and the number of cards in each deck are equal, therefore the the number of spades in this deck is 9.
In the first case, the 1st card is chosen(so the event has occurred and the probability is 1), and it is not a spade. So now from the remaining 35 cards we choose a card, which is a spade.(there are still 9 spades).
Therefore the probability = 9/35
In the second case, the 1st card is chosen(so the event has occurred and the probability is 1), and it is a spade. So now from the remaining 35 cards we choose a card, which is a spade.(there are now 8 spades left).
Therefore the probability = 8/35
Option D is the answer.
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