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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
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cm
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Can you compute that for me. Ty
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what is chemistry
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what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
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please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
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Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
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answer
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progressive wave
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fine, how about you?
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hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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Who can show me the full solution in this problem?
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Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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