Guided Learning Extension - Expected Value
Once you can figure out probability, you can use it to determine expected value. Expected value places different weights (money, points, etc.) on a particular probability of an outcome happening.
Example 1: You go to a carnival and decide to play a game that costs \(\$1\) to play. The game is to draw a card from a deck. If you draw a face card, you win \(\$1.50\). To calculate the expected value, we'd have to know the probability of drawing a face card, and the probability of not drawing a face card. We'll multiply the win or loss times the probability and add the values together to get the expected value of playing this game.
Step 1: Calculate the Probabilities
\(P\left(\text{Face}\right)=\large\frac{12}{52}=\frac{3}{13}\)
\(P\left(\text{Not a Face}\right)=\large\frac{40}{52}=\frac{10}{13}\)
Step 2: Multiply the probabilities times the gain or loss.
\(\large\frac{3}{13}(.5)=\normalsize.17\) (You paid \(\$1\) to play, but you win \(\$1.50\) so your total gain would be \(50\) cents).
\(\large\frac{10}{13}(-1)=\normalsize-.77\) (You paid \(\$1\) to play, so if you drew a card that was not a face card, you'd lose a dollar).
Step 3: Add the values together.
\(.17 + (-.77) = -.60\)
If you played this game multiples times, you'd expect to lose \(\$0.60\) each time you played.
Guided Learning
Once you can figure out probability, you can use it to determine expected value. Expected value places different weights (money, points, etc.) on a particular probability of an outcome happening.
Example 1: You go to a carnival and decide to play a game that costs \(\$1\) to play. The game is to draw a card from a deck. If you draw a face card, you win \(\$1.50\). To calculate the expected value, we'd have to know the probability of drawing a face card, and the probability of not drawing a face card. We'll multiply the win or loss times the probability and add the values together to get the expected value of playing this game.
Step 1: Calculate the Probabilities
\(P\left(\text{Face}\right)=\large\frac{12}{52}=\frac{3}{13}\)
\(P\left(\text{Not a Face}\right)=\large\frac{40}{52}=\frac{10}{13}\)
Step 2: Multiply the probabilities times the gain or loss.
\(\large\frac{3}{13}(.5)=\normalsize.17\) (You paid \(\$1\) to play, but you win \(\$1.50\) so your total gain would be \(50\) cents).
\(\large\frac{10}{13}(-1)=\normalsize-.77\) (You paid \(\$1\) to play, so if you drew a card that was not a face card, you'd lose a dollar).
Step 3: Add the values together.
\(.17 + (-.77) = -.60\)
If you played this game multiples times, you'd expect to lose \(\$0.60\) each time you played.
Guided Learning