"Is the Game Fair?" Statistics and Probability PPT Courseware 2

Description

"Is the Game Fair?" Statistics and Probability PPT Courseware 2

learning target

1. Be able to find the probability of simple events.

2. Through specific scenarios, students can further understand how to judge whether something is "economical", and then use it to judge the fairness of some game activities and modify game rules.

3. Enhance the ability to correctly judge and make decisions about some events in real life.

New course introduction

1. In a random event, if various situations are equally likely to occur, _______________ is often used to calculate the probability.

2. If the experiment is completed step by step, the probability is equal to ____________. If the experiment is classified, the probability is equal to ____________.

Knowledge explanation

Two students A and B are playing a dice game. Each of them rolls a dice.

(1) When the sum of the points of the two rolled dice is an odd number, A gets 1 point, otherwise B gets 1 point. Do you think this game is fair to both parties?

P A = P B = 1/2,

A and B each scored an average of 0.5 points each time.

Both sides have the same probability of winning, and the game is fair to both sides.

2) When the product of the points of the two rolled dice is an odd number, A gets 1 point, otherwise B gets 1 point. Do you think this game is fair to both parties? Why?

P A = 1/4, P B = 3/4.

A scores an average of 0.25 points each time, and B scores an average of 0.75 points each time. The game is unfair to both parties.

collaborative inquiry

Like everyone else, classmate A found that the rules of the above game (2) were not good for him. So classmate B said, "Well, when the product of the two dice is an odd number, you get 2 points, otherwise I get 1 point." .Do you think classmate A should accept this rule?

A gets an average of 0.5 points each time, and B gets an average of 0.75 points each time. A should not accept this rule.

How can the rules be changed to make the game fair for both parties?

Practice in class

1. (2011·Yiwu High School Entrance Examination) A certain school arranged three cars to organize ninth-grade students to go to the nursing home to participate in Lei Feng learning activities. Both Xiao Wang and Xiao Fei could choose one of these three cars to ride. Then Xiao Wang The probability of being in the same car with Xiao Fei is ( )

A.1/3 B.1/9 C.1/2 D.2/3

2. (2010·Qiandongnan Prefecture High School Entrance Examination) This is a two-person turntable game. There are three turntables that can rotate freely as shown in the picture. Two people, A and B, rotate the turntable. B records the number pointed when the pointer stops. When three If any of the numbers are the same, A wins, otherwise B wins.

Please draw a tree diagram to determine whether this game is fair and explain why.

3. (2010·Qinzhou High School Entrance Examination) There are 2 red balls and 1 yellow ball in the bag. They are all the same except for the color. Xiao Ming and Xiao Ying play a ball-touching game. The rules of the game are agreed upon: Xiao Ying starts from the bag. Xiao Ming takes out a ball at random, notes the color, and puts it back. Xiao Ming takes out another ball from the bag, notes the color, and puts it back. If the colors of the balls touched by two people are the same, Xiao Ying wins, otherwise Xiao Ming wins.

(1) Please use a tree diagram or column table method to represent all possible outcomes in a game;

(2) Are the rules of this game fair to both parties? Please explain the reason.

Summary of this lesson

1. In this lesson we learned how to judge whether something is "economical" and use it to judge the fairness of some game activities.

2. During the study of this class, I realized that in real life, judging whether an event is cost-effective or whether a game is fair cannot be judged only from the perspective of probability or points, but whether the final score values ​​​​are the same. be evaluated from this perspective.

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For more information about the PPT courseware "Is the Game of Statistics and Probability Fair?", please click the "Is the Game of Statistics and Probability Fair" ppt tag.

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Update Time: 2024-06-30

This template belongs to Mathematics courseware Beijing Normal University Ninth Grade Mathematics Volume 2 industry PPT template

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