# 11.7 Probability  (Page 5/18)

 Page 5 / 18

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.

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 $P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}$ probability of the union of two events $P\left(E\cup F\right)=P\left(E\right)+P\left(F\right)-P\left(E\cap F\right)$ probability of the union of mutually exclusive events $P\left(E\cup F\right)=P\left(E\right)+P\left(F\right)$ probability of the complement of an event $P\left(E\text{'}\right)=1-P\left(E\right)$

## 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] .

## 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 $\text{\hspace{0.17em}}1.\text{\hspace{0.17em}}$

What is a sample space?

What is an experiment?

An experiment is an activity with an observable result.

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

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 $\text{\hspace{0.17em}}0\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}1.\text{\hspace{0.17em}}$

## Numeric

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

Landing on red

can I see the picture
How would you find if a radical function is one to one?
how to understand calculus?
with doing calculus
SLIMANE
Thanks po.
Jenica
Hey I am new to precalculus, and wanted clarification please on what sine is as I am floored by the terms in this app? I don't mean to sound stupid but I have only completed up to college algebra.
I don't know if you are looking for a deeper answer or not, but the sine of an angle in a right triangle is the length of the opposite side to the angle in question divided by the length of the hypotenuse of said triangle.
Marco
can you give me sir tips to quickly understand precalculus. Im new too in that topic. Thanks
Jenica
if you remember sine, cosine, and tangent from geometry, all the relationships are the same but they use x y and r instead (x is adjacent, y is opposite, and r is hypotenuse).
Natalie
it is better to use unit circle than triangle .triangle is only used for acute angles but you can begin with. Download any application named"unit circle" you find in it all you need. unit circle is a circle centred at origine (0;0) with radius r= 1.
SLIMANE
What is domain
johnphilip
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This term is plural for a focus, it is used for conic sections. For more detail or other math questions. I recommend researching on "Khan academy" or watching "The Organic Chemistry Tutor" YouTube channel.
Chris
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what type of identity
Jeffrey
Confunction Identity
Barcenas
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meena
hello guys
meena
For each year t, the population of a forest of trees is represented by the function A(t) = 117(1.029)t. In a neighboring forest, the population of the same type of tree is represented by the function B(t) = 86(1.025)t.
by how many trees did forest "A" have a greater number?
Shakeena
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Kenard
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It's just like any other number. The important thing to know is that they exist and can be used in computations like any number.
Steve
I would like to add that they are used in AC signal analysis for one thing
Scott
Good call Scott. Also radar signals I believe.
Steve
They are used in any profession where the phase of a waveform has to be accounted for in the calculations. Imagine two electrical signals in a wire that are out of phase by 90°. At some times they will interfere constructively, others destructively. Complex numbers simplify those equations
Tim
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