Question

answer in the simplest way and like a teen can understand

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 — Why they’re not independent (simple):
- At the start there are 4 nines in 52 cards, so the chance any random card is a 9 is 4/52 = 1/13.
- If the first card Tim picked was a 9, there are now only 3 nines left in 51 cards. So the chance the second card is a 9 then is 3/51 = 1/17.
- 1/17 is different from 1/13, so knowing the first card was a 9 changes the chance the second is a 9. That means the two events are not independent.

Part B — How to make them independent:
- Put the first card back into the deck and reshuffle before picking the second card (sampling with replacement).
- Then the deck is back to 4 nines out of 52 for the second draw, so the second draw’s chance is 1/13 no matter what happened first — that makes the events independent.