A resort hotel has two station wagons, which it usesto shuttle its guests to and from the airport. If the largerof the two station wagons can carry five passengers andthe smaller can carry four passengers, the point (0, 3)represents the event that at a given moment the largerstation wagon is empty while the smaller one has threepassengers, the point (4, 2) represents the event that at the given moment the larger station wagon has four pas-sengers while the smaller one has two passengers, ... , draw a figure showing the 30 points of the correspondingsample space. Also, if E stands for the event that at leastone of the station wagons is empty, F stands for the eventthat together they carry two, four, or six passengers, and G stands for the event that each carries the same num-ber of passengers, list the points of the sample space that correspond to each of the following events:(a) E; (b) F; (c) G;(d) E ∪F; (e) E ∩F; (f) F ∪ G;(g) E ∪F; (h) E ∩ G ; (i) F ∩ E
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.
to shuttle its guests to and from the airport. If the larger
of the two station wagons can carry five passengers and
the smaller can carry four passengers, the point (0, 3)
represents the
station wagon is empty while the smaller one has three
passengers, the point (4, 2) represents the event that at
sengers while the smaller one has two passengers, ... ,
one of the station wagons is empty, F stands for the event
that together they carry two, four, or six passengers, and
ber of passengers, list the points of the sample space that
(a) E; (b) F; (c) G;
(d) E ∪F; (e) E ∩F; (f) F ∪ G;
(g) E ∪F
; (h) E ∩ G
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