Exercises
Build confidence in essential probability and statistics concepts with this introductory simulation quiz. Answer questions on fair-coin probabilities, dice outcomes, mutually exclusive events, expected value, and the probability of common results. Review core statistical ideas including the normal distribution and one standard deviation, p-values and null hypotheses, mode, range, and the effect of outliers on measures of central tendency. Ideal for students, beginners, and anyone preparing for an introductory math, data science, or statistics course.
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The probability of getting a head in a fair coin toss is 0.5 because there are two equally likely outcomes: head or tail.
There are 6 combinations to get a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). With 36 possible combos, the probability is 1/6.
In a normal distribution, 68% of data falls within one standard deviation of the mean due to the empirical rule.
A p-value less than 0.05 usually indicates that the null hypothesis can be rejected, suggesting a statistically significant result.
The mode is the number that appears most frequently. In the dataset 1, 2, 2, 3, 4, the number 2 appears twice.
The null hypothesis represents a statement of no effect or difference and is tested against the alternative hypothesis.
The mean is most affected by outliers because it includes all data points in its calculation, including extremes.
The range is the difference between the highest and lowest values. For the dataset 5, ..., 25, this is 25 - 5 = 20.
Mutually exclusive events cannot occur simultaneously. If one happens, the other doesn't, hence they are exclusive.
The expected value is the average value a random variable takes over many repetitions or trials.
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