A local radio station is staging a concert; it isn’t sure what music the band will play or how big the crowd will be. The table below shows the estimated profit from sales (in thousands of dollars) to the station depending on audience size and the type of music played (for example, if a “small” audience and classic rock, they will make $100K). Probability of music .2 .3 .5 Type of music Audience Size Small Moderate Large Classic Rock $100 $200 $300 Country $50 $250 $400 Hip Hop $30 $150 $500 Probability of size: .3 .4 .3 What is the probability that the audience size is not moderate? Which type of music gives the station the greatest chance of making $250K or greater from the concert? Assuming the type of music played and the audience size are probabilistically independent, what is the probability that a small audience shows up and ends up listening to Hip Hop?
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.
- A local radio station is staging a concert; it isn’t sure what music the band will play or how big the crowd will be. The table below shows the estimated profit from sales (in thousands of dollars) to the station depending on audience size and the type of music played (for example, if a “small” audience and classic rock, they will make $100K).
|
|
Type of music |
Audience Size |
||
|
Small |
Moderate |
Large |
|
|
Classic Rock |
$100 |
$200 |
$300 |
|
Country |
$50 |
$250 |
$400 |
|
Hip Hop |
$30 |
$150 |
$500 |
Probability of size: .3 .4 .3
What is the probability that the audience size is not moderate?
Which type of music gives the station the greatest chance of making $250K or greater from the concert?
Assuming the type of music played and the audience size are probabilistically independent, what is the probability that a small audience shows up and ends up listening to Hip Hop?
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