# Mathematics Questions and Answers – Bernoulli Trials and Binomial Distribution

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Bernoulli Trials and Binomial Distribution”.

1. What is the other name for Bernoulli trials?
a) Two-way experiment
b) Dichotomous experiment
c) Nucleo experiment
d) Three-way experiment

Explanation: Bernoulli trials is also called a Dichotomous experiment and is repeated n times. If in each trial the probability of success is constant, then such trials are called Bernoulli trails.

2. The term Bernoulli trials is termed after which swiss mathematician?
a) Jacob Bernoulli
b) Albert Einstein
c) Johann Gutenberg
d) Archimedes

Explanation: Bernoulli trials is termed after swiss mathematician Jacob Bernoulli. Bernoulli trials is also called a Dichotomous experiment and is repeated n times. If in each trial the probability of success is constant, then such trials are called Bernoulli trails.

3. Bernoulli trials only deal with mutually exclusive outcomes.
a) True
b) False

Explanation: A random experiment that has only two mutually exclusive outcomes called ‘success’ and ‘failure’. This experiment is called a Dichotomous experiment and is repeated n times. So, it is called as Bernoulli trials.

4. How many outcomes can a Bernoulli trial have?
a) 3
b) 2
c) 5
d) 2n

Explanation: Bernoulli trial has only two possible outcomes and is mutually exclusive. Those two outcomes are ‘success’ and ‘failure’. So, it is also called as a ‘yes’ or ‘no’ question.

5. Bernoulli trials are also called as _____ or _____ questions.
a) positive, negative
b) natural, whole
c) yes, no
d) mutually exclusive, mutually inclusive

Explanation: Bernoulli trials is also called a Dichotomous experiment and is repeated n times. Bernoulli trials is also called as a ‘yes’ or ‘no’ questions because it has only two outcomes, those are ‘success’ and ‘failure’.
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6. The Poisson distribution comes under which probability distribution?
a) Continuous probability distribution
b) Sine probability distribution
c) Discrete probability distribution
d) Mutual probability distribution

Explanation: Poisson distribution shows the number of times an event is likely to occur within a specified time. It is used only for independent events that occur at a constant rate within a given interval of time.

7. The Poisson distribution shows the number of times an event is likely to occur in a particular time interval.
a) False
b) True

Explanation: Poisson distribution is used for independent events and it shows the number of times an event is going to occur in specified intervals of time. The formula for Poisson distribution is P(x; μ) = (e) (μx) / x!

8. What is the formula for the Poisson distribution probability?
a) P(x; μ) = (e) (μx) / x!
b) P(x; μ) = (e-x) (μx) / x!
c) P(x; μ) = (e) (μ) / x!
d) P(x; μ) = (e) (μx) / x

Explanation: Poisson distribution shows the number of times an event is likely to occur within a specified time. The Poisson distribution probability formula is P(x; μ) = (e) (μx) / x!

9. What is the formula for binomial distribution?
a) P [X = x] = nCn px qn-x
b) P [X = x] = xCx px qn-x
c) P [X = x] = nCx px qn-x
d) P [X = x] = nCx pn qn-x

Explanation: Formula for binomial distribution is P [X = x] = nCx px qn-x
Where n is the number of trials, x is the number of successes and (n-x) is failures.

10. (n-x) is the number of successes in a binomial distribution.
a) False
b) True

Explanation: Formula for binomial distribution is P [X = x] = nCx px qn-x
Where n is the number of trials, x is the number of successes and (n-x) is failures.

11. P(x; μ) = (e) (μx) / x! is the formula for _____
a) parametric distribution
b) continuous distribution
c) poisson distribution
d) extreme distribution

Explanation: Poisson distribution shows the number of times an event is likely to occur within a specified time. The Poisson distribution probability formula is P(x; μ) = (e) (μx) / x!

12. P [X = x] = nCx px qn-x is the formula for _____
a) parametric distribution
b) binomial distribution
c) poisson distribution
d) extreme distribution

Explanation: Formula for binomial distribution is P [X = x] = nCx px qn-x
Where n is the number of trials, x is the number of successes and (n-x) is failures.

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