Question

answer in the simplest way and like a teen

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 different ​colored cards.
​He holds his selected card in his hand and chooses another ​card at random from the remaining cards in the deck.
​
​Part A
Explain why the events “Tim’s first card is a 9" and “Tim’s second ​card is a 9" are not independent.


0 Words
(b)

​Part B
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

Part A
They’re not independent because the first draw changes the deck. If the first card is a 9, there are only 3 nines left out of 51 cards, so
P(second is 9 | first is 9) = 3/51 = 1/17.
But overall P(second is 9) without knowing the first draw is 4/52 = 1/13. Since 1/17 ≠ 1/13, the first draw affects the chance of the second being a 9.

Part B
Put the first card back and reshuffle before the second draw (sampling with replacement). Then both draws have the same probabilities:
P(second is 9 | first is 9) = P(second is 9) = 4/52,
so the events become independent.