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Solving Grade 7 Math Problems Page 55 Workbook Volume 2 Connecting Knowledge: Familiarizing with the probability of events helps 6th-grade students refer to and understand how to solve exercises 8.4, 8.5, 8.6, 8.7 in the textbook lesson. Hence, when encountering similar exercises, students can do them.
For more good Grade 7 Math learning materials:
- Solving Grade 7 Math Problems Connecting Knowledge with Life
- Solving Grade 7 Math Problems Pages 7, 8 Workbook Volume 2 The Kite - Lesson 1: Collecting, Classifying, and Representing Data
- Solving Grade 7 Math Problems Pages 93, 94 Workbook Volume 2 Skyline Creative - Lesson 2: Familiarizing with the probability of random events
Solving Grade 7 Math Problems Page 55 Workbook Volume 2, Connecting Knowledge with Life
Familiarizing with the probability of events
1. Solving Exercise 8.4 Page 55 Math Textbook Grade 7
Problem: Mai and Viet each roll a die. Find the probabilities of the following events:
a) The total number of spots appearing on the two dice is greater than 1;
b) The product of the spots appearing on the two dice is greater than 36.
To solve: In a game or experiment, if there are k equally likely events and only one of these events always occurs, then the probability of each event is 1/k.
Answer:
a) When Mai and Viet each roll a die, the total number of dots appearing on two dice is always greater than 1. Therefore, the event 'The total number of dots appearing on two dice is greater than 1' is certain.
So the probability of 'the total number of dots appearing on two dice is greater than 1' is 1.
Solving guidance: In a game or experiment, if there are k equally probable events and only one of these events always occurs, then the probability of each event is 1/k.
Answer:
Consider the following events:
A: 'Paul selects the box of food with the Spanish flag'
B: 'Paul selects the box of food with the Dutch flag'
Since Paul can only choose 1 box, the probability of each event is equal and is 1/2.
So the probability of Paul predicting the Spanish team to win is 1/2.
3. Solve Problem 8.6 Page 55 Math Textbook Grade 7
Problem: A group of 7B students has 5 boys and 5 girls. The teacher randomly calls one student to the board for an exercise check. Consider the following two events:
A: 'The student called is a boy' and B: 'The student called is a girl'.
a) Are events A and B equally likely? Why?
b) Find the probability of event A and event B.
Solution: In a game or experiment, if there are k equally likely events and only one of these events always occurs, then the probability of each event is 1/k.
Answer:
Since the number of male and female students in the group is equal, the probability of each event is equal and is 1/2.
a) Events A and B are equally likely. Because the number of male and female students in the group is equal, the probability of each event is equal.
b) The probability of event A and event B is equal and is 1/2.
4. Solve Problem 8.7 Page 55 Math Textbook Grade 7
Problem: Roll a fair, balanced die. Find the probability of the following events:
A: 'The number of spots appearing on the die is less than 7';
B: 'The number of spots appearing on the die is 0';
C: 'The number of spots appearing on the die is 6'.
Solution: In a game or experiment, if there are k equally likely events and only one of these events always occurs, then the probability of each event is 1/k.
Answer:
A: The probability of 'The number of spots appearing on the die is less than 7' is 1 (Certain event).
B: 'The number of spots appearing on the die is 0' is 0 (Impossible event).
C: 'The number of spots appearing on the die is 6'.
Since each roll reveals only one face and there are 6 equally likely events, the probability of each event is equal and is 1/6.
