You are working at a game booth at your school's fair. To play the game, you toss quarters onto a table that has squares and circles on it. If a quarter lands completely in a circle, the player wins one dollar. You start to count the number of wins and losses. So far, there are 17 wins and 123 losses. What is the experimental probability that a person will win?
A. [tex]$P($[/tex] winning [tex]$)=\frac{1}{17}$[/tex] B. [tex]$P($[/tex] winning [tex]$)=\frac{17}{140}$[/tex] C. [tex]$P($[/tex] winning [tex]$)=\frac{123}{140}$[/tex] D. [tex]$P($[/tex] winning [tex]$)=\frac{1}{2}$[/tex]
Let's go through the steps to determine the experimental probability that a person will win when playing your game. We'll follow a logical sequence to arrive at the correct probability.
1. Count the Wins and Losses: - You have already counted the number of wins and losses so far. - Wins = 17 - Losses = 123
2. Calculate the Total Number of Plays: - Total plays is the sum of the wins and the losses. - Total plays = Wins + Losses = 17 + 123 = 140
3. Determine the Experimental Probability: - The experimental probability of an event is given by the number of successful outcomes divided by the total number of trials. - In this case, the successful outcome is winning, so the experimental probability of winning is: [tex]\[
P(\text{winning}) = \frac{\text{Number of wins}}{\text{Total number of plays}} = \frac{17}{140}
\][/tex]
4. Convert to Decimal Form (if needed): - To give a more intuitive understanding, you might want to convert this fraction to a decimal by performing the division. - [tex]\[
P(\text{winning}) = \frac{17}{140} \approx 0.1214
\][/tex]
Therefore, the experimental probability that a person will win the game is [tex]\(\frac{17}{140}\)[/tex] or approximately [tex]\(0.1214\)[/tex], which is about 12.14%.
