Three cards are drawn at random successively, with...

Name: Problem 6, Chapter 13: BUSINESS STATISTICS
Uploaded: 2021-12-12T07:05:22-08:00
Duration: 2 min 12 s
Channel: Hast Aggarwal
Description: Three cards are drawn at random successively, with replacement, from a well shuffled pack of cards. Getting 'a card of diamonds' is termed as a success. Obtain the probability distribution of the number of successes.

Three cards are drawn at random successively, with replacement, from a well shuffled pack of cards. Getting 'a card of diamonds' is termed as a success. Obtain the probability distribution of the number of successes.

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Key Concepts

Independent Trials

In probability theory, independent trials refer to experiments where the outcome of one trial does not affect the outcomes of other trials. In the context of the problem, each card is drawn with replacement, which ensures that the probability of drawing a diamond remains constant across draws, making each draw independent of the others.

Bernoulli Trial

A Bernoulli trial is an experiment that results in a binary outcome: success or failure. Here, drawing a diamond is considered a success, while drawing any other suit is a failure. Each draw from the deck qualifies as a Bernoulli trial because it has only two outcomes and a fixed probability of success.

Binomial Distribution

The binomial distribution describes the number of successes in a fixed number of independent Bernoulli trials. Since the problem involves drawing cards with replacement and counting the number of successes (diamonds) over a series of draws, the probability distribution of the number of successes exactly follows a binomial distribution with parameters corresponding to the number of trials and the probability of drawing a diamond in a single trial.

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