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When there are a fixed number of repeated trial of any experiments under identical conditions for which only one of two mutually exclusive outcomes, success or failure can result in each trial then
- a)Normal Distribution
- b)Binomial Distribution
- c)Poisson Distribution
- d)None is used
Correct answer is option 'B'. Can you explain this answer?
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When there are a fixed number of repeated trial of any experiments und...
Introduction:
The Binomial Distribution is a probability distribution that is used when there are a fixed number of repeated trial of any experiments under identical conditions for which only one of two mutually exclusive outcomes, success or failure can result in each trial.
Definition:
The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.
Characteristics:
The binomial distribution has the following characteristics:
- The trials are independent.
- There are a fixed number of trials.
- Each trial has only two possible outcomes: success or failure.
- The probability of success is constant for each trial.
- The trials are identical.
Example:
Suppose a coin is tossed 10 times. The probability of getting a head on each toss is 0.5. What is the probability of getting exactly 5 heads?
Solution:
Using the binomial distribution formula, we have:
P(X = 5) = (10 choose 5) * (0.5)^5 * (1-0.5)^5
= 252 * 0.03125 * 0.03125
= 0.2461
Therefore, the probability of getting exactly 5 heads in 10 tosses of a fair coin is 0.2461.
Conclusion:
The binomial distribution is a useful tool for calculating the probability of a certain number of successes in a fixed number of trials. It is widely used in various fields, including statistics, economics, and finance.
The Binomial Distribution is a probability distribution that is used when there are a fixed number of repeated trial of any experiments under identical conditions for which only one of two mutually exclusive outcomes, success or failure can result in each trial.
Definition:
The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure.
Characteristics:
The binomial distribution has the following characteristics:
- The trials are independent.
- There are a fixed number of trials.
- Each trial has only two possible outcomes: success or failure.
- The probability of success is constant for each trial.
- The trials are identical.
Example:
Suppose a coin is tossed 10 times. The probability of getting a head on each toss is 0.5. What is the probability of getting exactly 5 heads?
Solution:
Using the binomial distribution formula, we have:
P(X = 5) = (10 choose 5) * (0.5)^5 * (1-0.5)^5
= 252 * 0.03125 * 0.03125
= 0.2461
Therefore, the probability of getting exactly 5 heads in 10 tosses of a fair coin is 0.2461.
Conclusion:
The binomial distribution is a useful tool for calculating the probability of a certain number of successes in a fixed number of trials. It is widely used in various fields, including statistics, economics, and finance.
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When there are a fixed number of repeated trial of any experiments under identical conditions for which only one of two mutually exclusive outcomes, success or failure can result in each trial thena)Normal Distributionb)Binomial Distributionc)Poisson Distributiond)None is usedCorrect answer is option 'B'. Can you explain this answer?
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