What are the odds of correctly predicting the suit and number of 4 cards in a row from a deck of 52 cards?

Answer 1

The odds of correctly guessing the each card is 1/52, so the odd of guessing four in a row is (1/52)^4 = 1/7311616. This assumes the card is replaced and the deck is reshuffled each time. If the cards are not replaced, it is instead (1/52)(1/51)(1/50)(1/49) = 1/6497400, because there is one fewer card in the deck for each drawing.

Answer 2

It depends whether you mean:

(1) The first four cards in a row without replacement.

(2) The first four cards in a row with replacement and shuffling.

(3) Any four sequential cards while going through the deck guessing each one.

All three answers are different.

(1) is 1 in 52*51*50*49.
(2) is 1 in 52*52*52*52.
(3) is pretty complicated, though far more likely if you have a good memory for cards already seen.

Answer 3

1/52 * 1/51 * 1/50 * 1/49 = 1 / 6497400 = .0000001539

It seems reasonable to assume that this is without replacement.

Answer 4

the odds of each correct guess = 1/# of cards
so four correct guess
= (1/52)(1/51)(1/50)(1/49)
= 1/6497400
= 1.53907716932927 x 10^{-7 }

Answer 5

ZERO for the average person...100% for a magician...or card shark.

Answer 6

1:6,497,400...without replacement
1:7,311,616...with replacement