Question

Tim chooses one card at random from a deck of 52
cards, where each card ​has a single number from 1
to 13
and each number appears on 4
different ​colored cards.
​He holds his selected card in his hand and chooses another ​card at random from the remaining cards in the deck.

Describe one change that Tim can make before his second selection ​so that the events “Tim’s first card is a 9
" and “Tim’s second card is ​a 9
" will become independent.

Answer 1

Have Tim put his first card back into the deck and reshuffle (i.e. draw with replacement).

Reason: P(first is 9) = 4/52. After replacing, P(second is 9 | first is 9) = 4/52 = P(second is 9), so knowledge of the first draw does not change the probability of the second — the two events are independent.