completely useless.
When you pick an object and do not return it, in probability it is termed "without replacement".
If you draw 40 cards without replacement the probability is 1! If you draw just one, the probability is 1/4.
The probability, if you draw 40 cards, without replacement, is 1. That is, it is a certainty. The probability on a single random draw is 1/4.
Replacement mean we put "it" back before the next step. For example, in drawing cards, replacement means we put the card back before we draw another one. So given an arbitrary collection of objects we want to know what the probability of an event is with replacement. This is equivalent to saying what is the probability of an event when we remove an item from the collections, replace it, mix up the collection, and remove an item again. We can continue doing this infinite number of times.
completely useless.
When you pick an object and do not return it, in probability it is termed "without replacement".
The answer depends on how many cards are drawn, and whether they are drawn with or without replacement. If 1 card is drawn, the probability is 0, if 50 cards are drawn (without replacement), the probability is 1. If only two cards are drawn, at random and without replacement, the probability is (4/52)*(3/51) = 12/2652 = 0.0045
If you draw 40 cards without replacement the probability is 1! If you draw just one, the probability is 1/4.
The probability, if you draw 40 cards, without replacement, is 1. That is, it is a certainty. The probability on a single random draw is 1/4.
Replacement mean we put "it" back before the next step. For example, in drawing cards, replacement means we put the card back before we draw another one. So given an arbitrary collection of objects we want to know what the probability of an event is with replacement. This is equivalent to saying what is the probability of an event when we remove an item from the collections, replace it, mix up the collection, and remove an item again. We can continue doing this infinite number of times.
The probability of drawing aces on the first three draws is approx 0.0001810
If you pick enough cards, without replacement, the probability is 1. The probability for a single random draw is 1/26.
If five cards are drawn from a deck of cards without replacement, what is the probability that at least one of the cards is a heart?
Because with replacement, the total number of possible outcomes - the denominator of the probability ratio - remains the same. Without replacement the number of possible outcomes becomes smaller.
If 1 queen was drawn out of the 52 card deck without replacement, the probability of choosing a queen on the 2nd draw is 3/51 or 1/17.
The probability of drawing an Ace, King, and Queen from a standard deck of 52 cards, with replacement, is (4 in 52)3 or 64 in 140608, or 1 in 2197, or about 0.0004552.