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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 $\frac{1}{2}$ that the player moves forward $1$ space, and moving forward $2$ or $3$ spaces each have $\frac{1}{4}$ probability.
What is the expected value for the number of spaces a player moves forward on a turn?
spaces

Kayla is a basketball player who makes $50\mathrm{%}$ of her $2$-point shots and $20\mathrm{%}$ of her $3$-point shots.
problem a
Find Kayla's expected value for a $2$-point shot.
points

problem b
Find Kayla's expected value for a $3$-point shot.
points

problem c
Which type of shot should Kayla choose to score the most points?

## Want to join the conversation?

• 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.
• The idea ist that she will make half of her 2-point shots, scoring 2 points each, but also miss the other half, scoring 0 points each. So this, over time, will yield a result of approximately 1 point per shot.
• how do I find expected value
(1 vote)
• expected value = value*probability
• If E(X)= µ, what is E(X− µ) ?
(1 vote)
• 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!
• 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
• 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?
• How do you determine whether the odds are to your favor using the expected probability formula
(1 vote)
• oh i could've scrolled down here to get the answers the whole time, dang, missed opportunity
(1 vote)
• I finished it and it does not tell me that I have it done what do I do
(1 vote)
• For question 1, is the spinner fair ?
(1 vote)
• why the combined probability of 2 and 3-points are not 1?
(1 vote)
• What is expected value?