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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

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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.

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What is an experiment?

An experiment is an activity with an observable result.

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

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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.

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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

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How does twins formed
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They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
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Genetics is the study of heredity
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the study of living organisms and their interactions with one another and their environments
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the study of living organisms and their interactions with one another and their environment.
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list any five characteristics of the blood cells
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advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
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cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
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is like gone fail us
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cells is the basic structure and functions of all living things
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What is classification
ISCONT Reply
is organisms that are similar into groups called tara
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in what situation (s) would be the use of a scanning electron microscope be ideal and why?
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A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
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Diversity of living thing
ISCONT
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Cell division is the process by which a single cell divides into two or more daughter cells. It is a fundamental process in all living organisms and is essential for growth, development, and reproduction. Cell division can occur through either mitosis or meiosis.
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life is defined as any system capable of performing functions such as eating, metabolizing,excreting,breathing,moving,Growing,reproducing,and responding to external stimuli.
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Practice Key Terms 9

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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