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Explaining how to solve exercises 8.8, 8.9, 8.10, 8.11 on page 57 of the 7th-grade Math exercise book from Knowledge Connection, aiding students in easy homework completion and solidifying chapter knowledge.
Additional references for good 7th-grade Math resources include: - Solving 7th-grade Math exercises from the Knowledge Connection book with real-life applications. - Solving 7th-grade Math page 93, 94 exercises from the Creative Horizon book - Exercise 2: Getting familiar with the probability of random events.
Solving 7th-grade Math page 57 exercise 2 from the Knowledge Connection book with real-life connections.
1. Solving Exercise 8.8 Page 57 of Math Textbook for Grade 7
Problem: A bag contains cards labeled with numbers 9, 12, 15, 18, 21, 24. Drawing a card randomly from the bag. Choose the appropriate term (certain, impossible, random) to replace the '?' in the following sentences:
Event A: 'Drawing a card with an even number' is an event .?.
Event B: 'Drawing a card labeled with a number divisible by 3' is an event .?.
Event C: 'Drawing a card labeled with a number divisible by 10' is an event .?.
Solution Guide:
A certain event is an event that is known beforehand to always occur.
An impossible event is an event that is known beforehand to never occur.
A random event is an event that cannot be known beforehand whether it will occur or not.
Answer:
Event A: 'Drawing a card labeled with an even number' is a random event.
Event B: 'Drawing a card labeled with a number divisible by 3' is a certain event.
Event C: 'Drawing a card labeled with a number divisible by 10' is an impossible event.
2. Solving Exercise 8.9 Page 57 of Math Textbook for Grade 7
Problem: Each person rolls a die, one square and one round.
Find the probability to
a) The difference between the dots appearing on two dice is 6.
b) The number of dots appearing on two dice is less than 7 for each.
Solution Guide: In a game or experiment, if there are k equally likely events and only one event out of these k events always occurs, then the probability of each event is 1/k.
Answer:
a) The event 'The difference between the dots appearing on two dice is 6' is an impossible event because the maximum difference between the dots appearing on two dice is 5.
So the probability of 'The difference between the dots appearing on two dice is 6' is 0.
c) Event: 'The number of dots appearing on two dice is less than 7 for each' is a certain event because when Square and Circle each roll a die, the number of dots appearing can be 1, 3, 4, 5, or 6 dots, all less than 7.
So the probability of 'The number of dots appearing on two dice is less than 7 for each' is 1.
3. Solving Exercise 8.10 Page 57 of Math Textbook for Grade 7
Problem: In a box, there are 15 green balls and 15 red balls. Randomly pick one ball from the box. Consider the following two events:
A: 'Picking a red ball' and B: 'Picking a green ball'.
a) Are events A and B equally likely? Why?
b) Find the probability of events A and B.
Solution Guide:
In a game or experiment, if there are k equally likely events and only one event out of these k events always occurs, then the probability of each event is 1/k.
Answer:
a) Events A and B are equally likely. Because the number of green balls and the number of red balls are equal, the probabilities of the events are equal.
b) The probability of events A and B is equal and is 1/2.
4. Solving Exercise 8.11 Page 57 of Math Textbook for Grade 7
Problem: Randomly select a number from four numbers 11; 12; 13; and 14. Find the probability to
a) Selecting a number divisible by 5.
b) Selecting a number with two digits.
c) Selecting a prime number.
d) Selecting a number divisible by 6.
Solution Guide: In a game or experiment, if there are k equally likely events and only one event out of these k events always occurs, then the probability of each event is 1/k.
Answer:
a) The event 'Selecting a number divisible by 5' is an impossible event because all 4 numbers 11, 12, 13, and 14 are not divisible by 5.
The probability of 'Selecting a number divisible by 5' is 0.
b) The event 'Selecting a number with two digits' is a certain event because all 4 numbers 11, 12, 13, and 14 are two-digit numbers.
The probability of 'Selecting a number with two digits' is 1.
c) Selecting a prime number.
- Among the given numbers, we see that: numbers 11 and 13 are prime numbers.
d) Selecting a number divisible by 6.
- Among the given numbers, we see that: number 12 is divisible by 6.
Since only one number is selected from the four given numbers, the probability of 'Selecting a prime number' is 1/4.
This is the guidance for solving math problems for Grade 7 on page 57 of Volume 2. Students should refer to the solutions for Grade 7 math problems on page 58 of Volume 2 and review the exercises on page 55 of Volume 2 to reinforce their knowledge.
- Grade 7 Math Solutions on page 58 of Volume 2 of Knowledge Connection - Final exercises of Chapter 8
- Grade 7 Math Solutions on page 55 of Volume 2 of Knowledge Connection - Exercise 30: Getting acquainted with the probability of events
