According to an​ airline, flights on a certain route are on time 85​% of the time. Suppose 17 flights are randomly selected and the number of​ on-time flights is recorded.   ​(a) Explain why this is a binomial experiment. ​(b) Find and interpret the probability that exactly 12 flights are on time. ​(c) Find and interpret the probability that fewer than 12 flights are on time. ​(d) Find and interpret the probability that at least 12 flights are on time. ​(e) Find and interpret the probability that between 10 and 12 ​flights, inclusive, are on time. ​(a) Identify the statements that explain why this is a binomial experiment. Select all that apply.   A. There are two mutually exclusive​ outcomes, success or failure.   B. There are three mutually exclusive possibly​ outcomes, arriving​ on-time, arriving​ early, and arriving late.   C. Each trial depends on the previous trial.   D. The probability of success is the same for each trial of the experiment.   E. The trials are independent.   F. The experiment is performed until a desired number of successes is reached.   G. The experiment is performed a fixed number of times. ​(b) The probability that exactly 12 flights are on time is nothing. ​(Round to four decimal places as​ needed.)

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Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.