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A number x is selected from the numbers 1,2,3 and then a second number y is randomly selected from the numbers 1,4,9 what is the probability that product xy of the two numbers will be less than 9?
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A number x is selected from the numbers 1,2,3 and then a second number...
Step-by-step explanation:
Given : A number x is selected from the numbers 1,2,3 and then a second number y is randomly selected from the numbers 1,4,9.
Total number of outcomes for product of two numbers selected from x any :
3*3=9
The outcomes for which the product xy of the two numbers selected will be less than 9 : 1*1 , 1*4, 2*1, 2*4, 3*1
Hence, the number of desired outcomes = 5
Then, the probability that the product xy of the two numbers selected will be less than 9 :-
Community Answer
A number x is selected from the numbers 1,2,3 and then a second number...
Probability of Product xy being less than 9 when selecting two numbers from given sets
To find the probability that the product xy of two numbers will be less than 9, we need to consider all possible combinations of x and y and determine how many of them satisfy the given condition. Let's break down the problem step by step.
Step 1: Determine the sample space
The sample space is the set of all possible outcomes when selecting two numbers, one from each given set. In this case, the sample space consists of all combinations of x and y.
The possible values for x are 1, 2, and 3.
The possible values for y are 1, 4, and 9.
So, the sample space is:
{(1, 1), (1, 4), (1, 9), (2, 1), (2, 4), (2, 9), (3, 1), (3, 4), (3, 9)}
Step 2: Determine the favorable outcomes
We need to count the number of combinations (x, y) where the product xy is less than 9.
From the sample space, the combinations that satisfy the condition are:
{(1, 1), (1, 4), (1, 9), (2, 1), (2, 4), (2, 9), (3, 1), (3, 4)}
So, there are 8 favorable outcomes.
Step 3: Calculate the probability
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes (sample space).
Total number of possible outcomes = 9 (from the sample space)
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = 8/9
Therefore, the probability that the product xy of the two numbers will be less than 9 is 8/9.
Summary:
- Sample space: {(1, 1), (1, 4), (1, 9), (2, 1), (2, 4), (2, 9), (3, 1), (3, 4), (3, 9)}
- Favorable outcomes: {(1, 1), (1, 4), (1, 9), (2, 1), (2, 4), (2, 9), (3, 1), (3, 4)}
- Probability = 8/9
To find the probability that the product xy of two numbers will be less than 9, we need to consider all possible combinations of x and y and determine how many of them satisfy the given condition. Let's break down the problem step by step.
Step 1: Determine the sample space
The sample space is the set of all possible outcomes when selecting two numbers, one from each given set. In this case, the sample space consists of all combinations of x and y.
The possible values for x are 1, 2, and 3.
The possible values for y are 1, 4, and 9.
So, the sample space is:
{(1, 1), (1, 4), (1, 9), (2, 1), (2, 4), (2, 9), (3, 1), (3, 4), (3, 9)}
Step 2: Determine the favorable outcomes
We need to count the number of combinations (x, y) where the product xy is less than 9.
From the sample space, the combinations that satisfy the condition are:
{(1, 1), (1, 4), (1, 9), (2, 1), (2, 4), (2, 9), (3, 1), (3, 4)}
So, there are 8 favorable outcomes.
Step 3: Calculate the probability
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes (sample space).
Total number of possible outcomes = 9 (from the sample space)
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = 8/9
Therefore, the probability that the product xy of the two numbers will be less than 9 is 8/9.
Summary:
- Sample space: {(1, 1), (1, 4), (1, 9), (2, 1), (2, 4), (2, 9), (3, 1), (3, 4), (3, 9)}
- Favorable outcomes: {(1, 1), (1, 4), (1, 9), (2, 1), (2, 4), (2, 9), (3, 1), (3, 4)}
- Probability = 8/9
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A number x is selected from the numbers 1,2,3 and then a second number y is randomly selected from the numbers 1,4,9 what is the probability that product xy of the two numbers will be less than 9?
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A number x is selected from the numbers 1,2,3 and then a second number y is randomly selected from the numbers 1,4,9 what is the probability that product xy of the two numbers will be less than 9? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A number x is selected from the numbers 1,2,3 and then a second number y is randomly selected from the numbers 1,4,9 what is the probability that product xy of the two numbers will be less than 9? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number x is selected from the numbers 1,2,3 and then a second number y is randomly selected from the numbers 1,4,9 what is the probability that product xy of the two numbers will be less than 9?.
A number x is selected from the numbers 1,2,3 and then a second number y is randomly selected from the numbers 1,4,9 what is the probability that product xy of the two numbers will be less than 9? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A number x is selected from the numbers 1,2,3 and then a second number y is randomly selected from the numbers 1,4,9 what is the probability that product xy of the two numbers will be less than 9? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number x is selected from the numbers 1,2,3 and then a second number y is randomly selected from the numbers 1,4,9 what is the probability that product xy of the two numbers will be less than 9?.
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