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From Set A = {2, 3, 4, 5} and Set B = {11, 12, 13, 14, 15}, two numbers are randomly selected, one from each set. The probability that the sum of the two numbers equals 16 is ___. (Answer up to one decimal place)
Correct answer is '0.2'. Can you explain this answer?
Most Upvoted Answer
From Set A = {2, 3, 4, 5} and Set B = {11, 12, 13, 14, 15}, two numbe...
Set A = {2, 3, 4, 5}
Set B = {11, 12, 13, 14, 15}
Two numbers are chosen, one from set A and other from set B.
Then,
Total = 4 × 5 = 20 cases
Favourable case: Sum of two numbers equals 16.
{(5, 11), (4, 12), (3, 13), (2, 14)}
i.e. Number of favourable cases = 4
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Community Answer
From Set A = {2, 3, 4, 5} and Set B = {11, 12, 13, 14, 15}, two numbe...
Understanding the Problem
To find the probability that the sum of two randomly selected numbers, one from Set A and one from Set B, equals 16, we need to analyze the combinations.
Sets Defined
- Set A = {2, 3, 4, 5}
- Set B = {11, 12, 13, 14, 15}
Calculating Possible Combinations
1. Total Outcomes:
- The total number of ways to select one number from Set A and one number from Set B is:
- 4 (from Set A) × 5 (from Set B) = 20 total combinations.
2. Favorable Outcomes:
- We need to find pairs (a, b) such that a + b = 16:
- (2, 14): 2 + 14 = 16
- (3, 13): 3 + 13 = 16
- (4, 12): 4 + 12 = 16
- (5, 11): 5 + 11 = 16
- There are 4 favorable combinations.
Calculating Probability
- Probability Formula:
- Probability = (Number of Favorable Outcomes) / (Total Outcomes)
- Probability = 4 / 20 = 0.2
Final Result
The probability that the sum of the two numbers equals 16 is 0.2 or 20%.
To find the probability that the sum of two randomly selected numbers, one from Set A and one from Set B, equals 16, we need to analyze the combinations.
Sets Defined
- Set A = {2, 3, 4, 5}
- Set B = {11, 12, 13, 14, 15}
Calculating Possible Combinations
1. Total Outcomes:
- The total number of ways to select one number from Set A and one number from Set B is:
- 4 (from Set A) × 5 (from Set B) = 20 total combinations.
2. Favorable Outcomes:
- We need to find pairs (a, b) such that a + b = 16:
- (2, 14): 2 + 14 = 16
- (3, 13): 3 + 13 = 16
- (4, 12): 4 + 12 = 16
- (5, 11): 5 + 11 = 16
- There are 4 favorable combinations.
Calculating Probability
- Probability Formula:
- Probability = (Number of Favorable Outcomes) / (Total Outcomes)
- Probability = 4 / 20 = 0.2
Final Result
The probability that the sum of the two numbers equals 16 is 0.2 or 20%.
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