Notes On Bernoulli Trials - CBSE Class 12 Maths
A candidate can be selected for the MBBS course depending upon his or her performance in the entrance test. Thus, the answer to the question can be either yes or no. The newborn child can be either a girl or a boy. Thus, the answer to the question can be either yes or no. Observe that in each of the cases, there are only two possible outcomes. Let one of the outcomes be called a "success." For convenience, the happening or occurrence of a trial is considered a "success." Similarly, the other outcome is considered "not a success" or a "failure." Ex: In the first experiment of tossing a coin, if the occurrence of a head is considered a success, then the occurrence of a tail is a failure. If we perform this experiment any number of times, then each trial will have only two outcomes, success and failure. This means that these trials are independent, and hence, the outcome of one trial is independent of the outcome of the others. Independent trials having only two outcomes, namely success and failure, are called Bernoulli trials. The trials of a random experiment are said to be Bernoulli trials, if they satisfy the following conditions: • The number of trials should be finite. • The trials should be independent. • Each trial must have exactly two outcomes, success and failure. • The probability of success remains the same in each trial. Ex: Consider an experiment of throwing a fair die 10 times. Let's verify if the trials of the appearance of two on a die are Bernoulli trials. Let the event of getting a two in each trial be defined as success. Let the probability of success be p. Clearly, the successive throws are independent. ∴ p in the first throw = 1/2 p in the second throw = 1/2 Similarly, the probability of success or p remains the same for the other eight throws. Hence, the trials of getting a two are Bernoulli trials.

#### Summary

A candidate can be selected for the MBBS course depending upon his or her performance in the entrance test. Thus, the answer to the question can be either yes or no. The newborn child can be either a girl or a boy. Thus, the answer to the question can be either yes or no. Observe that in each of the cases, there are only two possible outcomes. Let one of the outcomes be called a "success." For convenience, the happening or occurrence of a trial is considered a "success." Similarly, the other outcome is considered "not a success" or a "failure." Ex: In the first experiment of tossing a coin, if the occurrence of a head is considered a success, then the occurrence of a tail is a failure. If we perform this experiment any number of times, then each trial will have only two outcomes, success and failure. This means that these trials are independent, and hence, the outcome of one trial is independent of the outcome of the others. Independent trials having only two outcomes, namely success and failure, are called Bernoulli trials. The trials of a random experiment are said to be Bernoulli trials, if they satisfy the following conditions: • The number of trials should be finite. • The trials should be independent. • Each trial must have exactly two outcomes, success and failure. • The probability of success remains the same in each trial. Ex: Consider an experiment of throwing a fair die 10 times. Let's verify if the trials of the appearance of two on a die are Bernoulli trials. Let the event of getting a two in each trial be defined as success. Let the probability of success be p. Clearly, the successive throws are independent. ∴ p in the first throw = 1/2 p in the second throw = 1/2 Similarly, the probability of success or p remains the same for the other eight throws. Hence, the trials of getting a two are Bernoulli trials.

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