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What is the difference between "exactly 3 successes" and "at least 3 successes" in 10 trials?

What is the difference between "exactly 3 successes" and "at least 3 successes" in 10 trials?
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Answer #1

Exactly 3 successes means , there are only and only 3 successes in 10 trials. There are exactly and appropriately 3 successes in 10 trials. If all the trials are independent, then the probability of getting exactly 3 successes in 10 trials is = 0.3

The concept of at least 3 successes is something different. It means that , you may have either 3 successes or more than 3 successes in 10 trials. You may have 3 success, 4 successes, 5 successes, 7 8 9 or 10 successes in 10 trials. If the trials are independent then the probability of getting at least 3 trials is greater than or equal to 0.3

The event "exactly 3 successes" is a particular case of the event "at least 3 successes" in 10 trials.

So the condition exactly 3 successes is a stronger condition. But "at least 3 successes" is a weaker condition.

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