Junior Achievement USA and the Allstate Foundation surveyed teenagers aged 14 to 18 and asked at what age they think they will become financially independent. The responses of 944 teenagers who answered this survey question as follows: Age Financially Independent, Number of Responses 16 to 20, 191 21 to 24, 467 25 to 27, 244 28 or older, 42 Consider the experiment of randomly selecting a teenager from the population of teenagers aged to 14 to 18. Required: a. Compute the probability of being financially independent for each of the four age categories. b. What is the probability of being financially independent before the age of 25? c. What is the probability of being financially independent after the age of 24? d. Do the probabilities suggest that the teenagers may be somewhat unrealistic in their expectations about when they will become financially independent?
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.
Junior Achievement USA and the Allstate Foundation surveyed teenagers aged 14 to 18 and asked at what age they think they will become financially independent. The responses of 944 teenagers who answered this survey question as follows:
Age Financially Independent, Number of Responses
16 to 20, 191
21 to 24, 467
25 to 27, 244
28 or older, 42
Consider the experiment of randomly selecting a teenager from the population of teenagers aged to 14 to 18.
Required:
a. Compute the
b. What is the probability of being financially independent before the age of 25?
c. What is the probability of being financially independent after the age of 24?
d. Do the probabilities suggest that the teenagers may be somewhat unrealistic in their expectations about when they will become financially independent?
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