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\dfrac12 that the player moves forward 11 space, and moving forward 22 or 33 spaces each have 14\dfrac14 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 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
spaces

Problem 2: Basketball decisions

Kayla is a basketball player who makes 50%50\% of her 22-point shots and 20%20\% of her 33-point shots.
problem a
Find Kayla's expected value for a 22-point shot.
If necessary, round your answer to the nearest tenth.
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
points

problem b
Find Kayla's expected value for a 33-point shot.
If necessary, round your answer to the nearest tenth.
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}
points

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