At the beginning of each year, my car is in good, fair, orbroken-down condition. A good car will be good at thebeginning of next year with probability .85; fair withprobability .10; or broken-down with probability .05. A faircar will be fair at the beginning of the next year withprobability .70 or broken-down with probability .30. It costs$6,000 to purchase a good car; a fair car can be traded infor $2,000; and a broken-down car has no trade-in value andmust immediately be replaced by a good car. It costs $1,000per year to operate a good car and $1,500 to operate a faircar. Should I replace my car as soon as it becomes a fair car,or should I drive my car until it breaks down? Assume thatthe cost of operating a car during a year depends on the typeof car on hand at the beginning of the year (after a new car,if any, arrives).
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.
At the beginning of each year, my car is in good, fair, or
broken-down condition. A good car will be good at the
beginning of next year with
probability .10; or broken-down with probability .05. A fair
car will be fair at the beginning of the next year with
probability .70 or broken-down with probability .30. It costs
$6,000 to purchase a good car; a fair car can be traded in
for $2,000; and a broken-down car has no trade-in value andmust immediately be replaced by a good car. It costs $1,000
per year to operate a good car and $1,500 to operate a fair
car. Should I replace my car as soon as it becomes a fair car,
or should I drive my car until it breaks down? Assume that
the cost of operating a car during a year depends on the type
of car on hand at the beginning of the year (after a new car,
if any, arrives).
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