Teenagers account for 10% of the US driving population, but 12% of all drivers in car accidents are teens. Each year 3% of all drivers are involved in a car accident. 1. Find the probability that a randomly selected driver in an accident is not a teen. 2. Find the probability that a randomly selected driver will be a teen who gets into an accident this year. 3. Find the probability that a randomly selected driver will get into an accident given that that person is a teen.
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.
Teenagers account for 10% of the US driving population, but 12% of all drivers in car accidents are teens. Each year 3% of all drivers are involved in a car accident.
1. Find the
2. Find the probability that a randomly selected driver will be a teen who gets into an accident this year.
3. Find the probability that a randomly selected driver will get into an accident given that that person is a teen.
4. Find the probability that a randomly selected driver will be a teen or will get into an accident this year.
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Given information:
Percentage of teenagers of the US driving population = 10%
Percentage teens out of all the drivers in car accidents = 12%
Percentage of all drivers involved in a car accident = 3%
Let T represent an event that a selected driver is a teenager.
Let C represent an event that a selected driver gets into an accident.
Symbolically,
It is required to obtain:
1. the probability that a randomly selected driver in an accident is not a teen.
2. the probability that a randomly selected driver will be a teen who gets into an accident this year.
3. the probability that a randomly selected driver will get into an accident given that the person is a teen.
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