independent
The second event is independent of the first.
Picking cards without replacing them are NOT independent events, since once you pick a card, you can't pick the same card again.
Spade: 1 in 4 Ace: 1 in 13
The answer depends on:whether or not the cards are drawn at random,whether or not the cards are replaced before drawing another,how many cards are drawn.If 45 cards are drawn, without replacement, the event is a certainty.
The answer depends on how many cards are drawn.
dependent
The second card cannot be the same as the first. Thus the first outcome affects the second and so the events are not independent.
The second event is independent of the first.
dependent
An independent probability is a probability that is not based on any other event.An example of an independent probability is a coin toss. Each toss is independent, i.e. not related to, any prior coin toss.An example of a dependent probability is the probability of drawing a second Ace from a deck of cards. The probability of the second Ace is dependent on whether or not a first Ace was drawn or not. (You can generalize this to any two cards because the sample space for the first card is 52, while the sample space for the second card is 51.)
Select 2 cards, do not put the 1st back in the deck. This is dependent probability. The outcome of drawing the 2nd card depends on the 1st card drawn. Select a card, look at it and put it back in the deck. Select a 2nd card. These are independent of each other. One does not change the probability for selecting the 2nd.
No, two events are independent if the outcome of one does not affect the outcome of the other. They may or may not have the same probability. Flipping two coins, or rolling two dice, are independent. Drawing two cards, however, are dependent, because the removal of the first card affects the possible outcomes (probability) of the second card.
Picking cards without replacing them are NOT independent events, since once you pick a card, you can't pick the same card again.
The probability of drawing a pair from a standard deck of 52 cards is 3 in 51, or 1 in 17, or about 0.0588.
The probability of drawing 3 cards, all with the value of 9, from a standard 52 card deck, is ~0.018%.
Spade: 1 in 4 Ace: 1 in 13
The probability of drawing a 10 out of 52 cards is 4 in 52, or 1 in 13, or about 0.07692.