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Key equations
probability of an event with equally likely outcomes
$$P(E)=\frac{n(E)}{n(S)}$$
probability of the union of two events
$$P(E\cup F)=P(E)+P(F)-P(E\cap F)$$
probability of the union of mutually exclusive events
$$P(E\cup F)=P(E)+P(F)$$
probability of the complement of an event
$$P(E\text{'})=1-P(E)$$
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
$\text{\hspace{0.17em}}0\text{\hspace{0.17em}}$ and
$\text{\hspace{0.17em}}1,\text{\hspace{0.17em}}$ inclusive of
$\text{\hspace{0.17em}}0\text{\hspace{0.17em}}$ and
$\text{\hspace{0.17em}}1.\text{\hspace{0.17em}}$
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
$\text{\hspace{0.17em}}A\text{}\text{and}B\text{\hspace{0.17em}}$ and a union of events
$\text{\hspace{0.17em}}A\text{and}B,\text{\hspace{0.17em}}$ the union includes either
$\text{\hspace{0.17em}}A\text{or}B\text{\hspace{0.17em}}$ 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
$\text{\hspace{0.17em}}0\text{\hspace{0.17em}}$ and
$\text{\hspace{0.17em}}1.\text{\hspace{0.17em}}$
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
hi vedant can u help me with some assignments
Solomon
find the 15th term of the geometric sequince whose first is 18 and last term of 387