During the play of a card game, you have seen 20 of the 52...

During the play of a card game, you have seen 20 of the 52 cards in the deck and none of them is the 4 of clubs. You need the 4 of clubs to win the game. What is the probability that you will win the game on the next card drawn?

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Key Concepts

Conditional Probability

Conditional probability is the measure of the likelihood of an event occurring given that another event has already occurred. When additional information becomes available — such as the observation of certain outcomes — the probability is recalculated based on the revised set of possibilities.

Sampling Without Replacement

Sampling without replacement refers to drawing items from a set in such a way that each item is not returned or reused after it is selected. This process reduces the total number of possible outcomes as items are removed from the sample, impacting subsequent probability calculations.

Reduced Sample Space

Reduced sample space is the concept of recalculating probabilities based only on the remaining possible outcomes after some outcomes have been observed or removed. This adjustment is crucial because the total number of events considered changes as information is gathered.

Uniform Probability Distribution

A uniform probability distribution assumes that each outcome in the remaining set is equally likely to occur. When no additional biases are introduced, it allows for straightforward computation of the likelihood of a specific event among the remaining possibilities.

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