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Key equations
probability of an event with equally likely outcomes
probability of the union of two events
probability of the union of mutually exclusive events
probability of the complement of an event
Key concepts
Probability is always a number between 0 and 1, where 0 means an event is impossible and 1 means an event is certain.
The probabilities in a probability model must sum to 1. See
[link] .
When the outcomes of an experiment are all equally likely, we can find the probability of an event by dividing the number of outcomes in the event by the total number of outcomes in the sample space for the experiment. See
[link] .
To find the probability of the union of two events, we add the probabilities of the two events and subtract the probability that both events occur simultaneously. See
[link] .
To find the probability of the union of two mutually exclusive events, we add the probabilities of each of the events. See
[link] .
The probability of the complement of an event is the difference between 1 and the probability that the event occurs. See
[link] .
In some probability problems, we need to use permutations and combinations to find the number of elements in events and sample spaces. See
[link] .
Section exercises
Verbal
What term is used to express the likelihood of an event occurring? Are there restrictions on its values? If so, what are they? If not, explain.
probability; The probability of an event is restricted to values between
and
inclusive of
and
The
union of two sets is defined as a set of elements that are present in at least one of the sets. How is this similar to the definition used for the
union of two events from a probability model? How is it different?
The probability of the
union of two events occurring is a number that describes the likelihood that at least one of the events from a probability model occurs. In both a union of sets
and a union of events
the union includes either
or both. The difference is that a union of sets results in another set, while the union of events is a probability, so it is always a numerical value between
and
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits
