Question

Suppose that 4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability that all 4 are spade?

Answer 1

There are 13 spades in a deck of 52 cards, so the probability of drawing one spade is 13/52 , or 1/4 . After drawing the first spade, there will be 12 spades left in a deck of 51 cards, so the probability of drawing the second spade is 12/51 , or 4/17 . The probability of drawing the third spade is 11/50 . The probability of drawing the fourth spade is 10/49 . So the probability of drawing four spades in a row is: (1/4).(4/17)⋅(11/50)⋅(10/49)=440/166600=11/4165≈0.00264 There is approximately a 0.3% chance of drawing four spades in a row, without replacement.