Determine whether the following probability experiment represents a binomial exp

Question

Determine whether the following probability experiment represents a binomial experiment and explain the reason for your answer. Seven cards are selected from a standard 52-card deck without replacement. The number of jacks selected is recorded. Does the probability experiment represent a binomial experiment? A. No, because the experiment is not performed a fixed number of times. O B. No, because the trials of the experiment are not independent and the probability of success differs from trial to trial. C. 0 D. No, because there are more than two mutually exclusive outcomes for each trial. Yes, because the experiment satisfies all the criteria for a binomial experiment.

Explanation / Answer

To be a binomial experiment, following conditions should be met.

i)

Trial are fixed and independent of one another.

ii)

Probability is same for each trial.

Since 7 cards are picked from a deck without replacement, for second trial number of

cards available is one less than previous trials because first card is not replaced.

This means that trials are not independent and probability differs from trial to trial.

Option B is correct

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