Under which of the following conditions may binomial distribution be used?

I. The number of trials is infinite and not fixed.

II. The trials are independent.

III. Each trial has two possible outcomes.

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A person X speaks the truth 4 out of 5 times and person Y speaks the truth 5 out of 6 times. What is the probability that they will contradict each other in stating the fact?

The probability that a student passes Physics test is 2/3 and the probability that he passes both Physics test and English test is 11/15. The probability that he passes at least one test is 4/5 What is the probability that he passes English test?

An event X can happen with probability pand event Y can happen with probability q. Further, X and Y are independent events. Which of the following statements is/are correct?

1. The probability that exactly one of the events happens is p + q - pq

II. The probability that at least one of the events happens is p + q - 2pq

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