<< Chapter < Page Chapter >> Page >

A child randomly selects 3 gumballs from a container holding 4 purple gumballs, 8 yellow gumballs, and 2 green gumballs.

  1. Find the probability that all 3 gumballs selected are purple.
  2. Find the probability that no yellow gumballs are selected.
  3. Find the probability that at least 1 yellow gumball is selected.

a 1 91 ; b 5 91 ; c 86 91

Got questions? Get instant answers now!

Access these online resources for additional instruction and practice with probability.

Visit this website for additional practice questions from Learningpod.

Key equations

probability of an event with equally likely outcomes P ( E ) = n ( E ) n ( S )
probability of the union of two events P ( E F ) = P ( E ) + P ( F ) P ( E F )
probability of the union of mutually exclusive events P ( E F ) = P ( E ) + P ( F )
probability of the complement of an event P ( E ' ) = 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 0 and 1 , inclusive of 0 and 1.

Got questions? Get instant answers now!

What is an experiment?

An experiment is an activity with an observable result.

Got questions? Get instant answers now!

What is the difference between events and outcomes? Give an example of both using the sample space of tossing a coin 50 times.

Got questions? Get instant answers now!

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 A     and  B and a union of events A   and   B , the union includes either A   or   B 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 0 and 1.

Got questions? Get instant answers now!

Numeric

For the following exercises, use the spinner shown in [link] to find the probabilities indicated.

A pie chart with eight pieces with one A colored blue, one B colored purple, once C colored orange, one D colored blue, one E colored red, one F colored green, one I colored green, and one O colored yellow.

Questions & Answers

a colony of bacteria is growing exponentially doubling in size every 100 minutes. how much minutes will it take for the colony of bacteria to triple in size
Divya Reply
what is the importance knowing the graph of circular functions?
Arabella Reply
can get some help basic precalculus
ismail Reply
What do you need help with?
Andrew
how to convert general to standard form with not perfect trinomial
Camalia Reply
can get some help inverse function
ismail
Rectangle coordinate
Asma Reply
how to find for x
Jhon Reply
it depends on the equation
Robert
whats a domain
mike Reply
The domain of a function is the set of all input on which the function is defined. For example all real numbers are the Domain of any Polynomial function.
Spiro
foci (–7,–17) and (–7,17), the absolute value of the differenceof the distances of any point from the foci is 24.
Churlene Reply
difference between calculus and pre calculus?
Asma Reply
give me an example of a problem so that I can practice answering
Jenefa Reply
x³+y³+z³=42
Robert
dont forget the cube in each variable ;)
Robert
of she solves that, well ... then she has a lot of computational force under her command ....
Walter
what is a function?
CJ Reply
I want to learn about the law of exponent
Quera Reply
explain this
Hinderson Reply
what is functions?
Angel Reply
A mathematical relation such that every input has only one out.
Spiro
yes..it is a relationo of orders pairs of sets one or more input that leads to a exactly one output.
Mubita
Is a rule that assigns to each element X in a set A exactly one element, called F(x), in a set B.
RichieRich
If the plane intersects the cone (either above or below) horizontally, what figure will be created?
Feemark Reply
Practice Key Terms 9

Get the best Precalculus course in your pocket!





Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Precalculus' conversation and receive update notifications?

Ask