Brainteaser 1657: Not a black and white case

From The Sunday Times, 12th June 1994 [link]

Marvo has been up to his tricks again. He shuffled a normal pack of 52 cards and then looked at each one in turn without letting Alice see them. In each case she had to predict whether the card was red or black and Marvo gave no indication of whether Alice’s guesses were right or wrong. But after 51 guesses Alice had guessed “black” 26 times and “red” 25 times and Marvo announced that Alice had exactly 10 predictions wrong so far.

(1) Which colour (if either) is more likely for Alice’s last card?

Marvo repeated the game with Bob. After 51 guesses Bob too had guessed “black” 26 times and “red” 25 times and Marvo announced that Bob had exactly 11 predictions wrong so far.

(2) Which colour (if either) is more likely for Bob’s last card?

Marvo then repeated the game once more with Carol. After 51 guesses Carol too had guessed “black” 26 times and “red” 25 times and Marvo announced that Carol had got at least 10 predictions wrong so far.

(3) Which colour (if either) is more likely for Carol’s last card?

This puzzle was included in the book Brainteasers (2002, edited by Victor Bryant). The puzzle text was, and the answers required were changed slightly, but the idea of the puzzle remains the same.

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