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Number of X is randomly selected from the set of odd numbers and Y is randomly selected from the set of even numbers of the set {1,2,3,4,5,6,7}.LetZ = (X+Y)..
What is P(Z= 5) equal to ?
- a)1/2
- b)1/3
- c)1/4
- d)1/6
Correct answer is option 'D'. Can you explain this answer?
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Number of X is randomly selected from the set of odd numbers and Y is ...
Set A = {1 ,2 ,3 ,4 ,5 ,6 ,7 } and z =x + y
x = set of odd numbers
y = set of even numbers
x = set of odd numbers
y = set of even numbers
Most Upvoted Answer
Number of X is randomly selected from the set of odd numbers and Y is ...
To find the probability P(Z=5), we need to determine the number of ways to select X and Y such that their sum is equal to 5, and then divide it by the total number of possible outcomes.
Number of Odd Numbers:
The set of odd numbers in the given set {1,2,3,4,5,6,7} is {1,3,5,7}. There are 4 odd numbers in this set.
Number of Even Numbers:
The set of even numbers in the given set {1,2,3,4,5,6,7} is {2,4,6}. There are 3 even numbers in this set.
Total Number of Possible Outcomes:
To find the total number of possible outcomes, we need to multiply the number of choices for X and Y. Since X is randomly selected from the set of odd numbers (4 choices) and Y is randomly selected from the set of even numbers (3 choices), the total number of possible outcomes is 4 * 3 = 12.
Number of Ways to Select X and Y such that X+Y=5:
To find the number of ways to select X and Y such that their sum is equal to 5, we can consider the following cases:
Case 1: X = 1, Y = 4
Case 2: X = 3, Y = 2
Therefore, there are 2 ways to select X and Y such that X+Y=5.
Calculating the Probability:
To calculate the probability P(Z=5), we divide the number of favorable outcomes (2) by the total number of possible outcomes (12).
P(Z=5) = 2/12
Simplifying the fraction, we get:
P(Z=5) = 1/6
Therefore, the correct answer is option 'D' (1/6).
Number of Odd Numbers:
The set of odd numbers in the given set {1,2,3,4,5,6,7} is {1,3,5,7}. There are 4 odd numbers in this set.
Number of Even Numbers:
The set of even numbers in the given set {1,2,3,4,5,6,7} is {2,4,6}. There are 3 even numbers in this set.
Total Number of Possible Outcomes:
To find the total number of possible outcomes, we need to multiply the number of choices for X and Y. Since X is randomly selected from the set of odd numbers (4 choices) and Y is randomly selected from the set of even numbers (3 choices), the total number of possible outcomes is 4 * 3 = 12.
Number of Ways to Select X and Y such that X+Y=5:
To find the number of ways to select X and Y such that their sum is equal to 5, we can consider the following cases:
Case 1: X = 1, Y = 4
Case 2: X = 3, Y = 2
Therefore, there are 2 ways to select X and Y such that X+Y=5.
Calculating the Probability:
To calculate the probability P(Z=5), we divide the number of favorable outcomes (2) by the total number of possible outcomes (12).
P(Z=5) = 2/12
Simplifying the fraction, we get:
P(Z=5) = 1/6
Therefore, the correct answer is option 'D' (1/6).
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