Question
Ten cards are selected out of a 52 card deck without replacement and the number of Jacks is observed. This is an example of a Binomial Experiment. true false
Ask by Chan Love. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
This is not a binomial experiment because the draws are dependent and the probability changes with each draw.
Solution
The statement is false.
Explanation:
For an experiment to be considered binomial, it must have a fixed number of independent trials with only two possible outcomes (often called "success" and "failure"), and the probability of success should be constant in each trial. When ten cards are drawn without replacement from a deck of 52 cards, the draws are dependent and the probability of drawing a Jack changes with each draw. Therefore, this situation is better modeled by a hypergeometric distribution, not a binomial distribution.
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Simplify this solution Extra Insights
False! While selecting cards and counting the number of Jacks resembles a binomial scenario, this situation is slightly different because the selection is made without replacement. In a binomial experiment, each trial is independent, but removing cards alters the probabilities of subsequent draws, making it a hypergeometric distribution instead. If you're ever unsure whether a situation fits into a binomial framework, remember to review whether conditions affect probability in subsequent selections. Understanding these distinctions can save you from calculation mishaps later on!
