Independent and dependent events

In Probability, if two events are not influenced by each other then they are independent.

Independent means not dependent.

Dependent means influenced or decided by something.

I’ll use a pack of cards to illustrate this idea. If I asked you to pick a card at random out of a standard pack of 52 playing cards, then the probability that you would pick an ace is 4/52 or 1/13. If the card was then returned to the pack and I asked you to pick a card again, then the probability of picking an ace would be 1/13 again. These two events are independent.

If though, after picking the first card, the card is not returned to the pack before the second card is picked, then what is the probability of picking an ace with your second pick?

Well, it depends. It depends on whether an ace was picked in the first pick. If the first card picked was not an ace then the probability of picking an ace on the second pick is 4/51. If the first card picked was an ace then the probability of picking an ace on the second pick is 3/51. These two events are not independent.