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What is the fundamental concept for probability and statistics?
The fundamental concept is that there are many processes in the world that contain a random element. If that were not the case, everything would be deterministic and there would be no need for probability of statistics.
What is a probability that a child would be a girl versus a boy?
It would depend on the parents' genes and age. Globally, the probability is approx 0.483
What is the probability that a family continue to have children until they have a boy will have more than three children?
The answer to this is 1 minus the probability that they will have 3 or fewer children. This would happen only if they had a boy as the first, second or third child. The probability they have a boy as first child is 0.5 The probability they have a boy as second is 0.25 The probability they have a boy as third is 0.125 Thus the total probability is 0.875 And so the probability they will have more than three children is 1-0.875 or 0.125
When a family of seven boys and no girls is expecting an eighth child what is the probability of the next child being a girl?
If the gender of a child were an independent variable then the genders of the existing children would be irrelevant and so the probability of the next child being a girl would be approximately 1/2.It would be approximately 1/2 because the overall proportion is not exactly half. However, and more important, is the fact that the gender of a child is affected by the parents' genes and so is not independent of the gender of previous children.
If a dice is rolled sixty times. Would you be sure to get ten 6's Explain your answer?
No, you could not be sure. There would be a high probability that you would roll ten but with a random event, you can never be sure of a specific outcome such as that.
