a) There are 62 million Americans who speak a language other than English at home. The languages are Spanish, Chinese Tagalog (Philippines language), Vietnamese, French, Korean, and others. Suppose that one of these individuals is selected at random. Use set notation to list the sample space. b) The numbers (in millions) of Americans speaking non-English languages at home are listed next. Language Spoken at Home Millions of Americans Spanish 38.4 Chinese 3.0 Tagalog 1.6 Vietnamese 1.4 French 1.3 Korean 1.1 Other 15.2 If one individual is selected at random find the probability of the following events. i. Individual speaks Spanish. ii. Individual speaks a language other than Spanish iii. Individual speaks Vietnamese or French
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) There are 62 million Americans who speak a language other than English at home. The
languages are Spanish, Chinese Tagalog (Philippines language), Vietnamese, French,
Korean, and others. Suppose that one of these individuals is selected at random. Use set
notation to list the sample space.
b) The numbers (in millions) of Americans speaking non-English languages at home
are listed next.
Language Spoken at Home Millions of Americans
Spanish 38.4
Chinese 3.0
Tagalog 1.6
Vietnamese 1.4
French 1.3
Korean 1.1
Other 15.2
If one individual is selected at random find the
i. Individual speaks Spanish.
ii. Individual speaks a language other than Spanish
iii. Individual speaks Vietnamese or French
iv. Individual speaks one of the other languages.
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