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A drawer holds 4 red hats and 4 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and immediately returning every hat to the drawer before taking out the next?
- a)1/8
- b)1/4
- c)1/2
- d)3/8
- e)7/12
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A drawer holds 4 red hats and 4 blue hats. What is the probability of ...
Getting three red out of 4 that are taken out has 4 options (4!/(3!*1!)) each option has a probability of (1/2)4 since drawing a red or blue has a 50% chance. 4*1/16= ¼ to get three red hats. The same goes for three blue hats so ¼+¼ =1/2.
Most Upvoted Answer
A drawer holds 4 red hats and 4 blue hats. What is the probability of ...
To find the probability of getting exactly three red hats or exactly three blue hats, we need to consider two different scenarios: getting three red hats and one blue hat, and getting three blue hats and one red hat.
Scenario 1: Three red hats, one blue hat
To calculate the probability of this scenario, we need to consider the number of ways we can choose three red hats out of four and one blue hat out of four.
- Number of ways to choose three red hats out of four: 4C3 = 4
- Number of ways to choose one blue hat out of four: 4C1 = 4
Therefore, the total number of ways to choose three red hats and one blue hat is 4 * 4 = 16.
Scenario 2: Three blue hats, one red hat
Similarly, to calculate the probability of this scenario, we need to consider the number of ways we can choose three blue hats out of four and one red hat out of four.
- Number of ways to choose three blue hats out of four: 4C3 = 4
- Number of ways to choose one red hat out of four: 4C1 = 4
Therefore, the total number of ways to choose three blue hats and one red hat is 4 * 4 = 16.
Total favorable outcomes:
The total number of favorable outcomes (i.e., scenarios where we get exactly three red hats or exactly three blue hats) is the sum of the favorable outcomes from both scenarios:
16 (scenario 1) + 16 (scenario 2) = 32
Total possible outcomes:
To find the total possible outcomes, we need to consider the number of ways we can choose four hats out of eight (since there are four red hats and four blue hats in the drawer):
Number of ways to choose four hats out of eight: 8C4 = 70
Probability:
The probability of getting exactly three red hats or exactly three blue hats is the ratio of the favorable outcomes to the total possible outcomes:
Probability = Favorable outcomes / Total possible outcomes = 32 / 70
Simplifying this fraction, we get 8/17, which is approximately equal to 0.47.
Since the question asks for the answer in the form of a fraction, we can further simplify the fraction by dividing both the numerator and denominator by 8:
Probability = 8/17 ≈ 1/2
Therefore, the correct answer is option C) 1/2.
Scenario 1: Three red hats, one blue hat
To calculate the probability of this scenario, we need to consider the number of ways we can choose three red hats out of four and one blue hat out of four.
- Number of ways to choose three red hats out of four: 4C3 = 4
- Number of ways to choose one blue hat out of four: 4C1 = 4
Therefore, the total number of ways to choose three red hats and one blue hat is 4 * 4 = 16.
Scenario 2: Three blue hats, one red hat
Similarly, to calculate the probability of this scenario, we need to consider the number of ways we can choose three blue hats out of four and one red hat out of four.
- Number of ways to choose three blue hats out of four: 4C3 = 4
- Number of ways to choose one red hat out of four: 4C1 = 4
Therefore, the total number of ways to choose three blue hats and one red hat is 4 * 4 = 16.
Total favorable outcomes:
The total number of favorable outcomes (i.e., scenarios where we get exactly three red hats or exactly three blue hats) is the sum of the favorable outcomes from both scenarios:
16 (scenario 1) + 16 (scenario 2) = 32
Total possible outcomes:
To find the total possible outcomes, we need to consider the number of ways we can choose four hats out of eight (since there are four red hats and four blue hats in the drawer):
Number of ways to choose four hats out of eight: 8C4 = 70
Probability:
The probability of getting exactly three red hats or exactly three blue hats is the ratio of the favorable outcomes to the total possible outcomes:
Probability = Favorable outcomes / Total possible outcomes = 32 / 70
Simplifying this fraction, we get 8/17, which is approximately equal to 0.47.
Since the question asks for the answer in the form of a fraction, we can further simplify the fraction by dividing both the numerator and denominator by 8:
Probability = 8/17 ≈ 1/2
Therefore, the correct answer is option C) 1/2.
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A drawer holds 4 red hats and 4 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and immediately returning every hat to the drawer before taking out the next?a)1/8b)1/4c)1/2d)3/8e)7/12Correct answer is option 'C'. Can you explain this answer?
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A drawer holds 4 red hats and 4 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and immediately returning every hat to the drawer before taking out the next?a)1/8b)1/4c)1/2d)3/8e)7/12Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A drawer holds 4 red hats and 4 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and immediately returning every hat to the drawer before taking out the next?a)1/8b)1/4c)1/2d)3/8e)7/12Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A drawer holds 4 red hats and 4 blue hats. What is the probability of getting exactly three red hats or exactly three blue hats when taking out 4 hats randomly out of the drawer and immediately returning every hat to the drawer before taking out the next?a)1/8b)1/4c)1/2d)3/8e)7/12Correct answer is option 'C'. Can you explain this answer?.
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