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A bag contains 5 black and 6 white balls; two balls are drawn at random. What is the probability that the balls drawn are white?
- a)10/11
- b)4/11
- c)6/11
- d)3/11
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A bag contains 5 black and 6 white balls; two balls are drawn at rando...
Given
Number of black balls = 5
Number of white balls = 6
Formula
Probability = Favorable events/Total possible events
Calculation
Favorable event = 6C2
Total possible events = 11C2
∴ Probability = 6C2/11C2 = (6 × 5)/(11 × 10) = 3/11
Most Upvoted Answer
A bag contains 5 black and 6 white balls; two balls are drawn at rando...
Understanding the Problem
A bag contains a total of 11 balls:
- 5 black balls
- 6 white balls
We need to find the probability that both balls drawn are white when two balls are drawn at random.
Total Ways to Draw Balls
To calculate the probability, we first determine the total number of ways to draw 2 balls from the 11 available.
- Total ways to choose 2 balls from 11:
- This can be calculated using the combination formula (n choose k), which for our case is C(11, 2).
Calculating Total Combinations
- Total combinations = C(11, 2) = (11 * 10) / (2 * 1) = 55
Favorable Outcomes
Next, we find the number of ways to draw 2 white balls from the 6 available.
- Ways to choose 2 white balls from 6:
- This is calculated as C(6, 2).
Calculating Favorable Combinations
- Favorable combinations = C(6, 2) = (6 * 5) / (2 * 1) = 15
Calculating Probability
Now, we can calculate the probability:
- Probability of drawing 2 white balls = (Number of favorable outcomes) / (Total outcomes)
- Probability = 15 / 55
Simplifying the Probability
- This simplifies to 3 / 11.
Conclusion
Thus, the probability that both balls drawn are white is:
- Probability = 3/11
The correct answer is option 'D'.
A bag contains a total of 11 balls:
- 5 black balls
- 6 white balls
We need to find the probability that both balls drawn are white when two balls are drawn at random.
Total Ways to Draw Balls
To calculate the probability, we first determine the total number of ways to draw 2 balls from the 11 available.
- Total ways to choose 2 balls from 11:
- This can be calculated using the combination formula (n choose k), which for our case is C(11, 2).
Calculating Total Combinations
- Total combinations = C(11, 2) = (11 * 10) / (2 * 1) = 55
Favorable Outcomes
Next, we find the number of ways to draw 2 white balls from the 6 available.
- Ways to choose 2 white balls from 6:
- This is calculated as C(6, 2).
Calculating Favorable Combinations
- Favorable combinations = C(6, 2) = (6 * 5) / (2 * 1) = 15
Calculating Probability
Now, we can calculate the probability:
- Probability of drawing 2 white balls = (Number of favorable outcomes) / (Total outcomes)
- Probability = 15 / 55
Simplifying the Probability
- This simplifies to 3 / 11.
Conclusion
Thus, the probability that both balls drawn are white is:
- Probability = 3/11
The correct answer is option 'D'.
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Community Answer
A bag contains 5 black and 6 white balls; two balls are drawn at rando...
Given
Number of black balls = 5
Number of white balls = 6
Formula
Probability = Favorable events/Total possible events
Calculation
Favorable event = 6C2
Total possible events = 11C2
∴ Probability = 6C2/11C2 = (6 × 5)/(11 × 10) = 3/11
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A bag contains 5 black and 6 white balls; two balls are drawn at random. What is the probability that the balls drawn are white?a)10/11b)4/11c)6/11d)3/11Correct answer is option 'D'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about A bag contains 5 black and 6 white balls; two balls are drawn at random. What is the probability that the balls drawn are white?a)10/11b)4/11c)6/11d)3/11Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains 5 black and 6 white balls; two balls are drawn at random. What is the probability that the balls drawn are white?a)10/11b)4/11c)6/11d)3/11Correct answer is option 'D'. Can you explain this answer?.
A bag contains 5 black and 6 white balls; two balls are drawn at random. What is the probability that the balls drawn are white?a)10/11b)4/11c)6/11d)3/11Correct answer is option 'D'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about A bag contains 5 black and 6 white balls; two balls are drawn at random. What is the probability that the balls drawn are white?a)10/11b)4/11c)6/11d)3/11Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains 5 black and 6 white balls; two balls are drawn at random. What is the probability that the balls drawn are white?a)10/11b)4/11c)6/11d)3/11Correct answer is option 'D'. Can you explain this answer?.
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