following events independent or dependent?

Question

a)rolling a 5 and then a 3 on a six sided dice?

 

 

B)pulling a card from a standard deck of 52 cards, replacing it and then pulling another card from the deck?

 

 

 

Answer 1

Hello, thank you for taking the time to post your question!

Both of these scenarios are examples of independent events! In scenario (a), the outcome of the first roll has no influence on the outcome of the second roll. Similarly in scenario (b), since the card has been replaced the 52 card deck has been restored to its original state. Meaning that the probability for any card will be the same on the second draw as it was on the first draw.

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Layne,

 

One way to think about this is: are the conditions for the second trial the same as the first?  If so, then the trials are independent.  But if trial 1 changes the conditions for trial 2, then the trials are dependent.

 

Thus, (a) is independent since the dice hasn't physically changed between the rolls, and the player has sort of randomized the dice in his cupped jiggling hands before each throw.

 

(b) is also independent since the card was replaced, so each draw is from a shuffled 52-card deck and the probabilities  of each type of card in the deck haven't changed.  But if you don't replace the card, then the second trial has modified probabilities based on only 51 possibilities in trial 2.