Three FM radio stations (A, B, and C) are competing for customers in the same market area. Through an aggressive advertising campaign, each month station A is capturing 7% of station B's customers and 5% of station C's customers. (Hint: The phrase "station A is capturing 7% of station B's customers" means that 7% of the listeners are moving from B to A, not the other way around.) At the same time, station A is losing only 2% of its customers to B and 2% of its customers to C. Additionally, each month 1% of B's customers switch to C, and 1% of C's customers switch to B. Initially, A and B each have 30% of the listeners and C has 40%. Use this information answer the following questions. (Give your answers correct to three decimal places. Note that you are asked to give decimal values and not percentages. For example, you would need to enter 0.628 as opposed to 62.800%.) (a) What fraction of the listeners will A have after 3 months? 900 (b) What fraction of the listeners will B have after 3 months? 270 (c) What fraction of the listeners will C have after 3 months?
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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