The Metropolis police station calls Superman an average of 3 times per hour to ask for his help. The probability that the station calls Superman in a time interval is dependent only on the length of the time interval and, furthermore, is independent of whether or not the department called Superman on any previous time interval. Superman goes on a date with Lois Lane and picks her up from her place at 7:00pm a) What is the probability that their date has been interrupted by 8:00pm? b) If the number of times he is called is independent from one hour to the next, what is the probability that Superman and Lois can finish their 4 hour date uninterrupted? c) What is the probability that the date is interrupted 5 times during the first hour and Lois decides to go back to the office and finish writing her article? d) What is the probability that the date is interrupted exactly 4 times during the first hour given that it is interrupted fewer than six times in the first hour? e) What is the average length of time Lois waits for Superman to be called away during the date?
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.
The Metropolis police station calls Superman an average of 3 times per hour to ask for his help. The probability that the station calls Superman in a time interval is dependent only on the length of the time interval and, furthermore, is independent of whether or not the department called Superman on any previous time interval. Superman goes on a date with Lois Lane and picks her up from her place at 7:00pm
a) What is the probability that their date has been interrupted by 8:00pm?
b) If the number of times he is called is independent from one hour to the next, what is the probability that Superman and Lois can finish their 4 hour date uninterrupted?
c) What is the probability that the date is interrupted 5 times during the first hour and Lois decides to go back to the office and finish writing her article?
d) What is the probability that the date is interrupted exactly 4 times during the first hour given that it is interrupted fewer than six times in the first hour?
e) What is the average length of time Lois waits for Superman to be called away during the date?
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