# 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 $\dfrac12$ that the player moves forward $1$ space, and moving forward $2$ or $3$ spaces each have $\dfrac14$ 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 $50\%$ of her $2$-point shots and $20\%$ of her $3$-point shots.
problem a
Find Kayla's expected value for a $2$-point shot.
Find Kayla's expected value for a $3$-point shot.