Question

for an in class demonstration, a teacher draws a card from a freshly shuffled deck. that card is a jack. the jack is not put back in the deck. a student states that the chance of drawing a king is now better than before. what, if anything, is incorrect about the students logic?

Answer 1

After one jack is removed the deck, the number of kings is unchanged, but the number of cards is reduced by one. The probability of drawing a king with another draw therefore has increased. In the limiting case, consider a 2 card deck containing 1 jack and 1 king. Draw the jack, set it aside, and draw again. The probability of drawing a king is very high :-)