Basics of Statistics and Probability MCQs

Basics of Statistics and Probability

Probability is simply how likely something is to happen.Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

The best example for understanding probability is flipping a coin:There are two possible outcomes—heads or tails.What’s the probability of the coin landing on Heads? We can find out using the equation P(H) = ?P(H)=?P, left parenthesis, H, right parenthesis, equals, question mark.You might intuitively know that the likelihood is half/half, or 50%.  But how do we work that out?  Probability =

Formula for calculating the probability of certain outcomes for an event

Formula for calculating the probability of certain outcomes for an eventIn this case:

Probability of a coin landing on heads

Probability of a coin landing on headsProbability of an event = (# of ways it can happen) / (total number of outcomes)P(A) = (# of ways A can happen) / (Total number of outcomes)Example 1There are six different outcomes.

Different outcomes rolling a die

Different outcomes rolling a dieWhat’s the probability of rolling a one?

Probability formula for rolling a '1' on a die

Probability formula for rolling a ‘1’ on a dieWhat’s the probability of rolling a one or a six?

Probability of a 1 or a 6 outcome when rolling a die

Probability of a 1 or a 6 outcome when rolling a dieUsing the formula from above:

Probability formula applied

Probability formula appliedWhat’s the probability of rolling an even number (i.e., rolling a two, four or a six)?

Probability of rolling an even number?  The formula and solution

Probability of rolling an even number? The formula and solutionTips

  • The probability of an event can only be between 0 and 1 and can also be written as a percentage.
  • The probability of event AAA is often written as P(A)P(A)P, left parenthesis, A, right parenthesis.
  • If P(A) > P(B)P(A)>P(B)P, left parenthesis, A, right parenthesis, is greater than, P, left parenthesis, B, right parenthesis, then event AAA has a higher chance of occurring than event BBB.
  • If P(A) = P(B)P(A)=P(B)P, left parenthesis, A, right parenthesis, equals, P, left parenthesis, B, right parenthesis, then events AAA and BBB  are equally likely to occur.

Assessment (Rules Of Probability)

1.__________ provides the summary statistics of data.

  1. Descriptive Statistics
  2. Inferential Statistics

Answer: 1)Descriptive Statistics

2.__________ is the process of applying logical or statistical techniques to evaluate and describe data in a meaningful way.

  1. Data Exploration
  2. Data Collection
  3. Data Analysis

Answer: 3)Data Analysis

3.__________ is an art of learning data.

  1. Statistics
  2. Probability
  3. Both the options
  4. None of the options

Answer: 1)Statistics

4.Descriptive Statistics works on __________ dataset.

  1. Sample
  2. Both the options
  3. Population

Answer: 1)Sample

5.__________ holds the responsibility of describing the data collected.

  1. Statistics
  2. None of the options
  3. Probability
  4. Both the optionsn

Answer: 1)Statistics

6.__________ contains all the elements of a dataset.

  1. None of the options
  2. Event
  3. Sample
  4. Population

Answer: 4)Population

Final Assessment
1.Any event containing two or more elements of the sample space is known as a ___________.

  1. Simple Event
  2. Mutually Exclusive Event
  3. Dependent Event
  4. Compound Event

Answer: 4)Compound Event

2.__________ calculates the number of events occurring in a specific period, when given the average number of times the event occurs in that time span.

  1. Binomial Distribution
  2. Poisson Distribution
  3. Normal Distribution
  4. Uniform Distribution

Answer: 2)Poisson Distribution

3.In a __________ experiment, each trial can result in either of the two outcomes only.

  1. Poisson
  2. Normal
  3. Binomial
  4. Uniform

Answer: 3)Binomial

4.__________ enable to observe data dispersion from a central point.

  1. None of the options
  2. Range, Standard Deviation, and Variance
  3. Range and Median
  4. Mean and Median
  5. Mean, Median, and Mode

Answer: 2)Range, Standard Deviation, and Variance

5.__________ represents the outcome of a statistical experiment in numerical values.

  1. Event
  2. Random Variable
  3. Sample
  4. Population

Answer: 2)Random Variable

6.The Hypothesis test process contains __________ steps.

  1. 3
  2. 4
  3. None of the options
  4. 5

Answer: 4)5

7.Null Hypothesis must be rejected if P-Value is __________ than Significance Level.

  1. Greater
  2. Lesser

Answer: 2)Lesser

8.The probability of committing a Type 1 error is called __________.

  1. Power of Test
  2. All the options
  3. None of the options
  4. Significance Level

Answer: 4)Significance Level

9.__________ helps to make inferences about a population.

  1. None of the options
  2. Inferential Statistics
  3. Descriptive Statistics
  4. All the options

Answer: 1)None of the options

10.Conditional Probability is denoted by __________.

  1. None of the options
  2. P(A|B)
  3. P(A AND B)
  4. P(A OR B)

Answer: 2)P(A|B)

11.When a probability function is used to describe a discrete probability distribution, it is called __________.

  1. Probability density function
  2. Cumulative Distributive Function
  3. Probability Mass Function
  4. None of the options

Answer: 3)Probability Mass Function

12.What variable can take only a countable number of values?

  1. All the options
  2. Discrete
  3. None of the options
  4. Continuous

Answer: 2)Discrete

13.P-Value measures the strength of evidence in support of a null hypothesis.

  1. False
  2. True
  3. 14.In a Binomial experiment, the letter P is used to denote __________.
  4. The probability of failure on an individual trial
  5. The probability of success on an individual trial
  6. Number of Trials
  7. None of the options

Answer: 1)False

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15.Measures of Central Tendency includes __________.

  1. Mean
  2. Median
  3. All the options
  4. Mode

Answer: 3)All the options

16.Null Hypothesis and Alternative Hypothesis must be __________.

  1. Non-mutually exclusive
  2. Mutually exclusive

Answer: 2)Mutually exclusive

17.If another event does not influence the occurrence of an event, it is called a Dependent Event.

  1. False
  2. True

Answer: 1)False

18.The __________ states that no significant difference exists between a set of variables.

  1. Alternative Hypothesis
  2. None of the options
  3. Null Hypothesis
  4. All the options

Answer: 3)Null Hypothesis

19.The letter e in a Poisson experiment denotes __________.

  1. All the options
  2. The mean number of successes that occur in a specified region
  3. The actual number of successes that occur in a specified region
  4. A constant whose value is approximately 2.71828
  5. None of the options

Answer: 4)A constant whose value is approximately 2.71828

20.Formal procedures used by statisticians to accept or reject hypotheses is called __________.

  1. None of the options
  2. Hypothesis Testing
  3. Statistical Hypothesis

Answer: 2)Hypothesis Testing

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