3-41. A commercial jet aircraft has four engines. For an aircraft in flight to land safely, at least two engines should be in working condition. Each engine has an inde- pendent reliability of p = 92%. a. What is the probability that an aircraft in flight can land safely? b. If the probability of landing safely must be at least 99.5%, what is the mini- mum value for p? Repeat the question for probability of landing safely to be 99.9%. c. If the reliability cannot be improved beyond 92% but the number of engines in a plane can be increased, what is the minimum number of engines that would achieve at least 99.5% probability of landing safely? Repeat for 99.9% probability. d. One would certainly desire 99.9% probability of landing safely. Looking at the answers to (b) and (c), what would you say is a better approach to safety, increasing the number of engines or increasing the reliability of each engine?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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