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The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of variables (x + y) being greater than 20 is (Answer up to two decimal places)
Correct answer is '0.25'. Can you explain this answer?
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Most Upvoted Answer
The variable x takes a value between 0 and 10 with uniform probabilit...
Consider x values on x-axis and y values on y-axis
0≤ x ≤ 10 and 0 ≤ y ≤ 20
Here x and y together constitute a rectangle given by OBPR.
Where, AB is the line x + y = 20
The probability of the sum of variables (x + y) being greater than 20 is given by
P[(x + y) > 20] = 
= 0.25
= 0.25Free Test
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Community Answer
The variable x takes a value between 0 and 10 with uniform probabilit...
Explanation:
Given Information:
- Variable x takes a value between 0 and 10 with uniform probability distribution.
- Variable y takes a value between 0 and 20 with uniform probability distribution.
Finding Probability of the Sum of Variables (x + y) being Greater than 20:
- To find the probability of the sum of variables (x + y) being greater than 20, we need to consider all possible combinations of x and y that satisfy this condition.
- The sum of x and y will be greater than 20 if x is greater than 10 or y is greater than 10.
- Since the probability distribution for both x and y is uniform, the probability of x being greater than 10 is 1/2 (10 out of the total range of 0-10), and the probability of y being greater than 10 is 1/2 (10 out of the total range of 0-20).
- The probability of the sum of variables (x + y) being greater than 20 can be calculated as the sum of the probabilities of x being greater than 10 and y being greater than 10, minus the probability of both x and y being greater than 10 (since we can only count it once).
- Therefore, the probability is 1/2 + 1/2 - 1/4 = 1/2 = 0.25.
Therefore, the probability of the sum of variables (x + y) being greater than 20 is 0.25.
Given Information:
- Variable x takes a value between 0 and 10 with uniform probability distribution.
- Variable y takes a value between 0 and 20 with uniform probability distribution.
Finding Probability of the Sum of Variables (x + y) being Greater than 20:
- To find the probability of the sum of variables (x + y) being greater than 20, we need to consider all possible combinations of x and y that satisfy this condition.
- The sum of x and y will be greater than 20 if x is greater than 10 or y is greater than 10.
- Since the probability distribution for both x and y is uniform, the probability of x being greater than 10 is 1/2 (10 out of the total range of 0-10), and the probability of y being greater than 10 is 1/2 (10 out of the total range of 0-20).
- The probability of the sum of variables (x + y) being greater than 20 can be calculated as the sum of the probabilities of x being greater than 10 and y being greater than 10, minus the probability of both x and y being greater than 10 (since we can only count it once).
- Therefore, the probability is 1/2 + 1/2 - 1/4 = 1/2 = 0.25.
Therefore, the probability of the sum of variables (x + y) being greater than 20 is 0.25.
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The variable x takes a value between 0 and 10 with uniform probability distribution. The variable y takes a value between 0 and 20 with uniform probability distribution. The probability of the sum of variables (x + y) being greater than 20 is (Answer up to two decimal places)Correct answer is '0.25'. Can you explain this answer?
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