Probability 03

Matching problem

Round table problem

Conditional probability

Let us toss 2 dice Each outcome (sum of two dice) has the probability of Let us now know the result of the first die, e.g. What is the probability of each outcome now? For the outcomes that are now impossible the probability is , for outcomes that are possible the probability is now Let denote the event and be a condition Then denotes the probability of event occurring under condition basically reduces the initial sample space to some subset

Examples

Joe is certain that his key is in the pockets of his jacket Joe is also sure that it is in the left pocket and sure that it is in the right pocket Joe is checking his left pocket, keys are not in the left pocket. What is the probability that the keys are now in the right pocket?

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There are 52 cards There are four players - North, South, East, West We know that North and South together have 8 spades What is the probability that East has three spades?

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What is the probability of drawing 2 red balls from the box with 8 red balls and 4 white balls?

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Multiplication rule theorem

Event independence definition

Hat-check problem

Then, what is the probability that exactly men have taken their own hat?

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Let there be 52 cards divided into 4 piles of 13 cards What is the probability that each pile has exactly one ace?

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Let there be a basketball quarter-final round, there are 8 teams 4 teams are strong and famous, say teams 1-4, 4 are no-name weaker teams What is the probability that none of the strong teams play against each other in the quarter-final?

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