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A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is a card of spade or an ace.
- a)4/13
- b)10/13
- c)26/13
- d)8/13
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A card is drawn at random from a well-shuffled deck of playing cards. ...
There are 52 cards in total.
Hence, total Outcomes =52
Probability of the card drawn is a card of spade or an Ace:
Total cards of Spade =13
Total Aces =4
Number of Aces of Spade =1
Therefore,
Probability of the card drawn is a card of spade or an Ace:
13/52 + 4/52 - 1/52 = 16/52 = 4/13
Most Upvoted Answer
A card is drawn at random from a well-shuffled deck of playing cards. ...
Probability of drawing a spade card:
There are 13 spade cards in a deck of 52 cards. Therefore, the probability of drawing a spade card is:
P(Spade) = Number of spade cards/Total number of cards = 13/52 = 1/4
Probability of drawing an Ace card:
There are 4 Ace cards in a deck of 52 cards. Therefore, the probability of drawing an Ace card is:
P(Ace) = Number of Ace cards/Total number of cards = 4/52 = 1/13
Probability of drawing a spade card or an Ace card:
To find the probability of drawing a spade card or an Ace card, we need to add the probabilities of drawing a spade card and an Ace card and subtract the probability of drawing a spade Ace card (i.e., the Ace of spades) because it has been counted twice.
P(Spade or Ace) = P(Spade) + P(Ace) - P(Spade and Ace)
Since the Ace of spades is both a spade card and an Ace card, we need to subtract the probability of drawing it once.
P(Spade or Ace) = 1/4 + 1/13 - 1/52 = 4/13
Therefore, the probability of drawing a card of spade or an Ace is 4/13.
There are 13 spade cards in a deck of 52 cards. Therefore, the probability of drawing a spade card is:
P(Spade) = Number of spade cards/Total number of cards = 13/52 = 1/4
Probability of drawing an Ace card:
There are 4 Ace cards in a deck of 52 cards. Therefore, the probability of drawing an Ace card is:
P(Ace) = Number of Ace cards/Total number of cards = 4/52 = 1/13
Probability of drawing a spade card or an Ace card:
To find the probability of drawing a spade card or an Ace card, we need to add the probabilities of drawing a spade card and an Ace card and subtract the probability of drawing a spade Ace card (i.e., the Ace of spades) because it has been counted twice.
P(Spade or Ace) = P(Spade) + P(Ace) - P(Spade and Ace)
Since the Ace of spades is both a spade card and an Ace card, we need to subtract the probability of drawing it once.
P(Spade or Ace) = 1/4 + 1/13 - 1/52 = 4/13
Therefore, the probability of drawing a card of spade or an Ace is 4/13.
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