## 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 eventIn this case:

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

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

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 dieUsing the formula from above:

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**Tips**

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

**Assessment (Rules Of Probability)**

1.__________ provides the summary statistics of data.

- Descriptive Statistics
- 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.

- Data Exploration
- Data Collection
- Data Analysis

**Answer: 3)Data Analysis**

3.__________ is an art of learning data.

- Statistics
- Probability
- Both the options
- None of the options

**Answer: 1)Statistics**

4.Descriptive Statistics works on __________ dataset.

- Sample
- Both the options
- Population

**Answer: 1)Sample**

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

- Statistics
- None of the options
- Probability
- Both the optionsn

**Answer: 1)Statistics**

6.__________ contains all the elements of a dataset.

- None of the options
- Event
- Sample
- Population

**Answer: 4)Population**

**Final Assessment**

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

- Simple Event
- Mutually Exclusive Event
- Dependent Event
- 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.

- Binomial Distribution
- Poisson Distribution
- Normal Distribution
- Uniform Distribution

**Answer: 2)Poisson Distribution**

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

- Poisson
- Normal
- Binomial
- Uniform

**Answer: 3)Binomial**

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

- None of the options
- Range, Standard Deviation, and Variance
- Range and Median
- Mean and Median
- Mean, Median, and Mode

**Answer: 2)Range, Standard Deviation, and Variance**

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

- Event
- Random Variable
- Sample
- Population

**Answer: 2)Random Variable**

6.The Hypothesis test process contains __________ steps.

- 3
- 4
- None of the options
- 5

**Answer: 4)5**

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

- Greater
- Lesser

**Answer: 2)Lesser**

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

- Power of Test
- All the options
- None of the options
- Significance Level

**Answer: 4)Significance Level**

9.__________ helps to make inferences about a population.

- None of the options
- Inferential Statistics
- Descriptive Statistics
- All the options

**Answer: 1)None of the options**

10.Conditional Probability is denoted by __________.

- None of the options
- P(A|B)
- P(A AND B)
- 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 __________.

- Probability density function
- Cumulative Distributive Function
- Probability Mass Function
- None of the options

**Answer: 3)Probability Mass Function**

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

- All the options
- Discrete
- None of the options
- Continuous

**Answer: 2)Discrete**

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

- False
- True
- 14.In a Binomial experiment, the letter P is used to denote __________.
- The probability of failure on an individual trial
- The probability of success on an individual trial
- Number of Trials
- None of the options

**Answer: 1)False**

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15.Measures of Central Tendency includes __________.

- Mean
- Median
- All the options
- Mode

**Answer: 3)All the options**

16.Null Hypothesis and Alternative Hypothesis must be __________.

- Non-mutually exclusive
- Mutually exclusive

**Answer: 2)Mutually exclusive**

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

- False
- True

**Answer: 1)False**

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

- Alternative Hypothesis
- None of the options
- Null Hypothesis
- All the options

**Answer: 3)Null Hypothesis**

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

- All the options
- The mean number of successes that occur in a specified region
- The actual number of successes that occur in a specified region
- A constant whose value is approximately 2.71828
- 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 __________.

- None of the options
- Hypothesis Testing
- Statistical Hypothesis

**Answer: 2)Hypothesis Testing**