#1
What is the probability of rolling a 6 on a fair six-sided die?
1/6
Explanation1 out of 6 possible outcomes is a 6.
#2
In a standard deck of playing cards, how many face cards are there?
12
ExplanationThere are 3 face cards (jack, queen, king) in each of the 4 suits.
#3
What is the probability of drawing a red card from a standard deck of 52 cards?
1/4
ExplanationThere are 26 red cards out of 52 in a standard deck.
#4
What is the mode of the following set of numbers: {4, 6, 6, 8, 9, 9, 9, 11}?
9
ExplanationThe mode is the value that appears most frequently in a set of numbers.
#5
What is the probability of rolling an odd number on a fair six-sided die?
1/3
ExplanationThere are 3 odd numbers (1, 3, 5) out of 6 possible outcomes.
#6
What is the mean of the following set of numbers: {2, 4, 6, 8, 10}?
8
ExplanationThe mean is the average, calculated by adding all numbers and dividing by the count.
#7
Which distribution is commonly used to model the number of successes in a fixed number of independent Bernoulli trials?
Binomial distribution
ExplanationThe binomial distribution models the number of successes in a fixed number of trials.
#8
A coin is flipped three times. What is the probability of getting exactly two heads?
1/8
ExplanationThere are 3 ways to get exactly 2 heads: HHT, HTH, THH, out of 8 possible outcomes.
#9
Which of the following is NOT a measure of central tendency?
Variance
ExplanationVariance measures the spread or dispersion of a set of data, not its central tendency.
#10
What is the standard deviation of the numbers 1, 3, 5, 7, 9?
3
ExplanationStandard deviation measures the spread of data around the mean.
#11
What is the expected value of a discrete random variable?
The average value over many trials
ExplanationThe expected value is the average outcome over many repetitions of the experiment.
#12
What is the area under the normal distribution curve?
1
ExplanationThe total area under the normal curve is always 1, representing the entire probability space.
#13
In hypothesis testing, what does the p-value represent?
Probability of observing the data given that the null hypothesis is true
ExplanationThe p-value indicates the strength of evidence against the null hypothesis.
#14
What is the complement of an event?
The probability of the event not occurring
ExplanationThe complement of an event is 1 minus the probability of the event occurring.
#15
What is the significance level in hypothesis testing?
The probability of making a Type I error
ExplanationThe significance level is the probability of rejecting the null hypothesis when it is true.