Three cards are drawn at random one after another from a...

Name: Problem 25, Chapter 21: Business Mathematics and Statistics
Uploaded: 2021-07-22T01:44:16-08:00
Duration: 1 min 58 s
Channel: Goutam Chand
Description: Three cards are drawn at random one after another from a full pack of Playing Cards. What is the probability that (i) the first two are spades and the third is a heart, (ii) two are spades and one is a heart?

Three cards are drawn at random one after another from a full pack of Playing Cards. What is the probability that (i) the first two are spades and the third is a heart, (ii) two are spades and one is a heart?

Key Concepts

Probability

Probability is the measure of how likely an event is to occur. It quantifies the chance of an outcome occurring within a defined sample space and is typically calculated by dividing the number of favorable outcomes by the number of all possible outcomes.

Conditional Probability

Conditional probability is the probability of an event occurring given that another event has already occurred. This concept is crucial when dealing with sequential events where the outcome of one event affects the total outcomes available for subsequent events, such as drawing cards without replacement.

Multiplication Principle

The multiplication principle allows the computation of the probability of a sequence of events by multiplying the probability of each event. When events are dependent—as in the case of successive draws from a deck without replacement—each probability is adjusted to reflect the outcomes of the previous events.

Combinatorial Analysis

Combinatorial analysis is the branch of mathematics concerned with counting, both as a means and an end in obtaining probabilities. It involves determining the number of favorable outcomes and the total number of possible outcomes using tools like combinations and permutations, especially when order matters in sequential draws.

Hypergeometric Distribution

The hypergeometric distribution is a discrete probability distribution used for scenarios involving draws without replacement from a finite population. It provides the probability of drawing a specific number of successes (e.g., certain card suits) in a given number of draws, making it highly relevant in card-drawing problems.

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