Question

You randomly draw three cards from a normal deck of 52 cards. What is the probability that the first card is not a spade, thesecond card is a spade, and the third card is also a spade if you do not replace the first or second card? Enter your answeras a decimal rounded to the nearest thousandth.

Answer 1

Total number of cards in the normal deck is 52

Number of spades in the normal deck = 13

Probability of drawing a spade(first card) = 13/52 = 1/4

Probability of not drawing a spade(first card) = 1 - 1/4 = 3/4

Since the first card is not replaced,

number of cards left = 52 - 1 = 51

number of spades left = 13

Probability of drawing a spade(second card) = 13/51

Since the second card is not replaced,

total number of cards left = 51 - 1 = 50

number of spades left = 13 - 1 = 12

Probability that the third card is a spade = 12/50 = 6/25

Thus, the probability that the first card is not a spade, the second card is a spade, and the third card is also a spade = 3/4 x 13/51 x 6/25 = 0.046