MAKING PREDICTIONS WITH EXPERIMENTAL PROBABILITY

A simulation is a model of an experiment that would be difficult or inconvenient to actually perform. You can use a simulation to find an experimental probability and make a prediction.

Thew formula given below can be used to find experimental probability. 

Example 1 :

A baseball team has a batting average of 0.250 so far this season. This means that the team’s players get hits in 25% of their chances at bat. Use a simulation to predict the number of hits the team’s players will have in their next 34 chances at bat.

Solution : 

Step 1 : 

Choose a model.

Batting average  =  0.250  =  250/1000  =  1/4

A standard deck of cards has four suits, hearts, diamonds, spades, and clubs. Since 1/4 of the cards are hearts, you can let hearts represent a “hit.” Diamonds, clubs, and spades then represent “no hit.”

Step 2 : 

Perform the simulation.

Draw a card at random from the deck, record the result, and put the card back into the deck. Continue until you have drawn and replaced 34 cards in all. 

(H = heart, D = diamond, C = club, S = spade)

H  D  D  S  H  C  H  S  D  H  C  D  C  C  D  H  H

S  D  D  H  C  C  H  C  H  H  D  S  S  S  C  H  D

Step 2 : 

Make a prediction.

Count the number of hearts in the simulation.

Because there are 11 hearts, you can predict that the team will have 11 hits in its next 34 chances at bat.

Example 2 :

A toy machine has equal numbers of red, white, and blue foam balls which it releases at random. Ross wonders which color ball will be released next. Describe how you could use a standard number cube to predict the answer.

Solution : 

Let 1 and 2 represent red, 3 and 4 represent white, and 5 and 6 represent blue. Toss the cube 50 times to determine the experimental probability for each color.

Predict that the next ball will be the color with the greatest experimental probability.

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