The National Longitudinal Study of Adolescent Health interviewed several thousand teens (grades 7 to 12). One question asked was “What do you think are the chances you will be married in the next 10 years?” Here is a two-way table of the responses by gender: Opinion Female Male Almost no chance 121 83 Some chance but probably not 136 154 A 50-50 chance 464 498 A good chance 753 691 Almost certain 1176 761 How many individuals are described in this table? How many females were among the respondents? The percent of females among the respondents was about %.
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 National Longitudinal Study of Adolescent Health interviewed several thousand teens (grades 7 to 12). One question asked was “What do you think are the chances you will be married in the next 10 years?” Here is a two-way table of the responses by gender:
| Opinion | Female | Male |
|---|---|---|
| Almost no chance | 121 | 83 |
| Some chance but probably not | 136 | 154 |
| A 50-50 chance | 464 | 498 |
| A good chance | 753 | 691 |
| Almost certain | 1176 | 761 |
- How many individuals are described in this table?
- How many females were among the respondents?
- The percent of females among the respondents was about %.
- Your percent from the previous exercise is part of
- the conditional distribution of sex among adolescents with a given opinion.
- the marginal distribution of opinion about marriage.
- the marginal distribution of sex.
- What percent of females thought that they were almost certain to be married in the next 10 years?
% - Your percent from the previous exercise is part of
- the conditional distribution of opinion about marriage among women.
- the marginal distribution of opinion about marriage.
- the conditional distribution of sex among those who thought they were almost certain to be married.
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