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What is the Probability of drawing two spades out of 52 cards?
The probability of drawing a spade in a standard 52 card deck is 13 in 52, or 1 in 4. The probability of drawing a second spade, assuming the first spade was not replaced back into the deck, is 12 in 51. The probability, then, of drawing two spades is the product of those two probabilities, or 12 in 204, or 1 in 17.
What is the probability of choosing a red spade?
The probability of drawing a red spade is zero. There are no red spades in a standard deck.
Are mutually exclusive events also complementary events?
Not necessarily. The probability of a complementary event with probability p is 1-p. Two mutually exclusive events, however, don't necessarily add up to a probability of 1. For example, the probability of drawing a King from a standard deck of cards is 1 in 13, which the complementary probability of not drawing a King is 12 in 13. The probability, however, of drawing a Heart is 1 in 4, while the probability of drawing a Club is also 1 in 4. That leaves Diamonds and Spades, which account for the remaining probability of 2 in 4.
What is the probability of drawing a king and a diamond from a deck of playing cards?
The probability of drawing a king is 4:52The probability of drawing a diamond is 13:52 (or 1:4)The probability of drawing a king (0.07692...) then replacing that king into the deck then drawing a diamond is 0.019230769.If you leave the king out, the probability will be slightly greater (4/52) * (13/51)Unless the king you left out of the deck was a king of diamonds, in which case, the probability would be (4/52) * (12/51)
What are the odds against drawing a spade greater than 3 and less than 9?
The probability of drawing a 4, 5, 6, 7, or 8 of spades is 5 in 52. The probability of not drawing a 4, 5, 6, 7, or 8 of spades, therefore, is (52-5) in 52, or 47 in 52, or about 0.9038.
