Question

Rick organized three games for a club's 25th anniversary celebration.

Get-It-Rolling is a game in which the player rolls an eight-sided die. The player wins if the die lands on 5.
Bag-of-Tokens is a game in which the player draws a token from a bag containing 7 tokens, each of a different color. The player wins if they draw the red token.
Pick-Your-Tile is a game in which the player picks a number tile from a box of 12 tiles, each with a different number on it. The player wins if they pick the tile that has the number 9 on it.
Rick kept track of wins and losses for each game attempt in the following table.

Game Number of Wins Number of Losses
Get-It-Rolling (A) 26 173
Bag-of-Tokens (B) 54 141
Pick-Your-Tile (C) 17 175

Select the correct statement.

A.
The results from both game B and game C align closely with the theoretical probability of winning those games, while the results from game A do not.
B.
Only the results from game A align closely with the theoretical probability of winning that game.
C.
The results from both game A and game C align closely with the theoretical probability of winning those games, while the results from game B do not.
D.
Only the results from game B align closely with the theoretical probability of winning that game.

Answer 1

Answer: C. The results from both game A and game C align closely with the theoretical probability of winning those games, while the results from game B do not.

Explanation: I got it right on PLATO, but here's the actual explanation as well.

For game A, you have a 1 in 8 chance to land on 5, so you're going to do 1/8 which = .125 or 12.5%. Now you're going to do the number of wins divided by the total number of attempts. In this case, it'll be 26/199 (199 came from 26+173). This equals .131 or 13.1% which is really close to 12.5% and thus aligned closely with the theoretical probability of rolling a 5 on an 8 sided die.

You follow this same process for the other two games, doing 1/7 for the second game and 1/12 for the third, and then using their respective results.

Answer 2

The correct statement is C. The results from both games A and game C align closely with the theoretical probability of winning those games, while the results from game B do not.

I was given it right on PLATO, but right here's the real rationalization as properly. For recreation A, you have got a 1 in 8 threat to land on 5, so you're going to do 1/8 which =  125 or 12.5%. Now you'll do the wide variety of wins divided by the whole number of attempts. In this example, it is going to be 26/199 (199 came from 26+173). This equals .131 or 13.1% which is clearly close to 12.5% and accordingly aligned carefully with the theoretical possibility of rolling a five on an eight-sided die. You follow this identical technique for the opposite video games, doing 1/7 for the second recreation and 1/12 for the third, after which the usage of their respective results.

What is an example of theoretical probability?

The theoretical possibility is determined through the sample area of an item. For an instance, the probability of rolling a three with the use of a truthful die is 1/6. Which is due to the fact that quantity 3 represents one viable final result out of the 6 possible outcomes of rolling a fair die.

The theoretical probability is based totally on the belief that results have an equal danger of happening even as empirical chance is primarily based on the observations of an experiment. There are two other varieties of possibilities and those are axiomatic probability and subjective chance.

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