Chance Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
In a game, you roll a die. If you roll 6, you win \5.Otherwiseyoulose. Otherwise you lose \11. Calculate the expected value per game and determine if the game is fair.

Solution

  1. 1
    P(win)=16P(\text{win}) = \frac{1}{6}; P(lose)=56P(\text{lose}) = \frac{5}{6}
  2. 2
    Expected value: E=16(5)+56(โˆ’1)=56โˆ’56=0E = \frac{1}{6}(5) + \frac{5}{6}(-1) = \frac{5}{6} - \frac{5}{6} = 0
  3. 3
    The expected value is \$0 per game โ€” perfectly fair
  4. 4
    Fair game: in the long run, neither player gains an advantage on average

Answer

Expected value = \$0 per game; this is a fair game.
A fair game has expected value of zero โ€” no systematic advantage for either player. Expected value = sum of (outcome ร— probability) for all outcomes. Positive EV favors the player; negative EV favors the house.

About Chance

Chance describes the inherent randomness in outcomes of experiments โ€” the fact that even with complete knowledge, some events cannot be predicted with certainty.

Learn more about Chance โ†’

More Chance Examples

Example 1 easy

A bag contains 3 red, 2 blue, and 5 green marbles. Find the probability of randomly drawing a red ma

Example 2 medium

Weather forecasts say 70% chance of rain tomorrow. Explain what this probability means in terms of r

Example 3 easy

A spinner has 8 equal sections numbered 1โ€“8. Find (a) [formula] and (b) [formula].

โ† All Chance Examples Chance Concept

Related Concepts

ProbabilityRisk