CDF of

HypergeometricDistribution is an example of a right continuous function:

Suppose an urn has 100 elements, of which 40 are special:

The probability distribution that there are 20 special elements in a draw of 50 elements:

Compute the probability that there are more than 25 special elements in a draw of 50 elements:

Compute the expected number of special elements in a draw of 50 elements:

Suppose there are 5 defective items in a batch of 10 items, and 6 items are selected for testing. Simulate the process of testing when the number of defective items found is counted:

Find the probability that there are 2 defective items in the sample:

Find the distribution of the number of spades in a five-card poker hand:

Find the probability that there are at least 2 spades in the poker hand:

A lottery sells 10 tickets for $1 per ticket. Each time there is only one winning ticket. A gambler has $5 to spend. Find his probability of winning if he buys 5 tickets in 5 different lotteries:

His probability of winning is greater if he buys 5 tickets in the same lottery:

An urn contains

white balls and 1 blue ball. Two players draw balls from the urn without replacement until the blue ball is drawn. The player who draws the blue ball wins. Find the chance of winning for the player who draws the first ball. Assuming the first player wins at the

draw, the probability that the

previous draws were all white follows

HypergeometricDistribution:

The conditional probability of drawing a blue ball given that the previous

balls were white:

The resulting probability is a sum over

:

When the number of white balls is odd, both players have an equal chance of winning:

When the number of white balls is even, the game is unfair: