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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= 11) equal to ?
- a)0
- b)1/4
- c)1/6
- d)1/12
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
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
Z > 11 is only possible when x = 7 and y = 6
x = set of odd numbers
y = set of even numbers
Z > 11 is only possible when x = 7 and y = 6
Most Upvoted Answer
Number of X is randomly selected from the set of odd numbers and Y is ...
Problem:
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}. Let Z = (X Y). What is P(Z = 11) equal to?
Solution:
To find the probability P(Z = 11), we need to determine the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determining the favorable outcomes
The value of Z will be 11 if the sum of X and Y is equal to 11. Let's consider the possible combinations of X and Y that satisfy this condition:
- X = 1, Y = 10
- X = 3, Y = 8
- X = 5, Y = 6
Therefore, there are 3 favorable outcomes.
Step 2: Determining the total number of possible outcomes
X is randomly selected from the set of odd numbers {1, 3, 5, 7}, and Y is randomly selected from the set of even numbers {2, 4, 6}. The total number of possible outcomes is given by the product of the number of elements in each set:
Total number of possible outcomes = 4 (odd numbers) * 3 (even numbers) = 12
Step 3: Calculating the probability
The probability P(Z = 11) is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:
P(Z = 11) = Number of favorable outcomes / Total number of possible outcomes
= 3 / 12
= 1 / 4
Therefore, the correct answer is option 'D' - 1/12.
Summary:
- The probability P(Z = 11) is equal to the ratio of the number of favorable outcomes (3) to the total number of possible outcomes (12).
- By simplifying the ratio, we find that P(Z = 11) = 1/4.
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}. Let Z = (X Y). What is P(Z = 11) equal to?
Solution:
To find the probability P(Z = 11), we need to determine the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determining the favorable outcomes
The value of Z will be 11 if the sum of X and Y is equal to 11. Let's consider the possible combinations of X and Y that satisfy this condition:
- X = 1, Y = 10
- X = 3, Y = 8
- X = 5, Y = 6
Therefore, there are 3 favorable outcomes.
Step 2: Determining the total number of possible outcomes
X is randomly selected from the set of odd numbers {1, 3, 5, 7}, and Y is randomly selected from the set of even numbers {2, 4, 6}. The total number of possible outcomes is given by the product of the number of elements in each set:
Total number of possible outcomes = 4 (odd numbers) * 3 (even numbers) = 12
Step 3: Calculating the probability
The probability P(Z = 11) is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:
P(Z = 11) = Number of favorable outcomes / Total number of possible outcomes
= 3 / 12
= 1 / 4
Therefore, the correct answer is option 'D' - 1/12.
Summary:
- The probability P(Z = 11) is equal to the ratio of the number of favorable outcomes (3) to the total number of possible outcomes (12).
- By simplifying the ratio, we find that P(Z = 11) = 1/4.
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