Q: Two bad eggs are mixed with 10 good ones. Three eggs are drawn at random without replacement Prepare probability distribution table for the no of bad eggs?

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The binomial distribution is a discrete probability distribution which describes the number of successes in a sequence of draws from a finite population, with replacement. The hypergeometric distribution is similar except that it deals with draws without replacement. For sufficiently large populations the Normal distribution is a good approximation for both.

completely useless.

When you pick an object and do not return it, in probability it is termed "without replacement".

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 you draw 40 cards without replacement the probability is 1! If you draw just one, the probability is 1/4.

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The binomial distribution is a discrete probability distribution which describes the number of successes in a sequence of draws from a finite population, with replacement. The hypergeometric distribution is similar except that it deals with draws without replacement. For sufficiently large populations the Normal distribution is a good approximation for both.

completely useless.

with replacement: binominal distribution f(k;n,p) = f(0;5,5/12) without replacement: hypergeometric distribution f(k;N,m,n) = f(0;12,5,5)

hypergeometric distribution f(k;N,n,m) = f(1;51,3,1) or binominal distribution f(k;n,p) = f(1;1,3/51) would result in same probability

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

hypergeometric distribution f(k;N,n,m) = f(3;52,4,3)

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 aces on the first three draws is approx 0.0001810

The answer depends on how many cards are drawn.