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Expected value (basic)

Expected value uses probability to tell us what outcomes to expect in the long run.

Problem 1: Board game spinner

A board game uses the spinner shown below to determine how many spaces a player will move forward on each turn. The probability is 12 that the player moves forward 1 space, and moving forward 2 or 3 spaces each have 14 probability.
What is the expected value for the number of spaces a player moves forward on a turn?
If necessary, round your answer to the nearest hundredth.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
spaces

Problem 2: Basketball decisions

Kayla is a basketball player who makes 50% of her 2-point shots and 20% of her 3-point shots.
problem a
Find Kayla's expected value for a 2-point shot.
If necessary, round your answer to the nearest tenth.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
points

problem b
Find Kayla's expected value for a 3-point shot.
If necessary, round your answer to the nearest tenth.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
points

problem c
Which type of shot should Kayla choose to score the most points?
Choose 1 answer:

Want to join the conversation?

  • leaf green style avatar for user Chip Mattis
    Wouldn't the expected value for a 2-point shot be 2 points? I understand what you're getting at, but this seems like asking what color Napoleon's white horse was.
    (22 votes)
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  • blobby green style avatar for user bgrooms6278
    how do I find expected value
    (1 vote)
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  • marcimus pink style avatar for user HBarakzay
    If E(X)= µ, what is E(X− µ) ?
    (1 vote)
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    • primosaur seed style avatar for user Ian Pulizzotto
      The expected value of a difference is the difference of the expected values, and the expected value of a non-random constant is that constant. Note that E(X), i.e. the theoretical mean of X, is a non-random constant.
      Therefore, if E(X) = µ, we have E(X − µ) = E(X) − E(µ) = µ − µ = 0.

      Have a blessed, wonderful day!
      (12 votes)
  • male robot hal style avatar for user AlAbbas14
    Hi just wondering what year/s is mathematics II ? and does anyone know any helpful sites i can do a exam of mathmatics 2 ?
    #YouCanLearnAnything
    thanks
    (3 votes)
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    • leaf green style avatar for user astro648
      It varies, you can find it in highschool courses but it covers a wide range of topics that are in a wide range of grades like it covers both probability, geometry, and trigonometry which varies across different grade levels and courses for those respective grade levels. Sorry for the 2 year late reply but...well...better late than never, right?
      (6 votes)
  • eggleston blue style avatar for user daniel zhang
    How do you determine whether the odds are to your favor using the expected probability formula
    (1 vote)
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    • blobby green style avatar for user daniella
      In order to determine whether the odds are in your favor using the expected probability formula, you need to compare the expected value (or mean) with the potential outcomes. If the expected value is higher than the current situation or the alternative options, then the odds are generally in your favor. Conversely, if the expected value is lower, then the odds may not be as favorable.

      For example, in Problem 2, Kayla's expected value for a 2-point shot is 1 point, while for a 3-point shot, it's 0.6 points. If Kayla consistently makes 2-point shots, she can expect to score an average of 1 point per shot. If she consistently makes 3-point shots, she can expect to score an average of 0.6 points per shot. Therefore, she should choose the option with the higher expected value to maximize her scoring potential.
      (1 vote)
  • blobby green style avatar for user Tue Pham
    In problem 1, can someone reinterpret the problem please? Isn't that space 1 , 2 or 3 just the name of the certain area of the board game spinner? Why do we multiply the name by its probability ? I really don't understand the problem. Thanks in advance.
    (0 votes)
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    • aqualine tree style avatar for user Mark Thomas
      Hi Tue Pham! When you spin the spinner, the result tells you how many spaces you get to move forward on an imaginary game board. Imagine a game where your goal is to get from "point A" to "point B", and to get there you move a certain number of spaces each turn. Sort of like this:

      START --- ( A )  ---  ( B ) --- ( C ) --- ( D ) --- END

      If you spin and get a "3", you would move from START to A, B, and finally land on C (you would move 3 spaces forward). Does that help clarify?
      (3 votes)
  • male robot hal style avatar for user emilio.wendlandt
    I finished it and it does not tell me that I have it done what do I do
    (1 vote)
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  • blobby green style avatar for user e.guzman209209
    For question 1, is the spinner fair ?
    (1 vote)
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  • aqualine ultimate style avatar for user Leon
    why the combined probability of 2 and 3-points are not 1?
    (1 vote)
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    • blobby green style avatar for user daniella
      The combined probability of Kayla making a 2-point shot and a 3-point shot is not necessarily equal to 1 because she might miss both types of shots. In this scenario, if Kayla misses both types of shots, the combined probability would be less than 1.

      It's important to understand that the probabilities provided represent the likelihood of specific outcomes (i.e., making a 2-point shot or making a 3-point shot) and do not necessarily guarantee that one of the outcomes will occur. The sum of these probabilities indicates the total probability space for all possible outcomes, but it doesn't have to equal 1 in this case because there are other potential outcomes not explicitly mentioned (such as missing both types of shots).
      (1 vote)
  • aqualine ultimate style avatar for user John He
    What is expected value?
    (0 votes)
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