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A drawer contains 12 red and 12 blue socks, all unmatched. A person takes socks out at random in the dark. How many socks must he take out to be sure that he has at least two blue socks?
- a)18
- b)35
- c)28
- d)14
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A drawer contains 12 red and 12 blue socks, all unmatched. A person ta...
Problem:
A drawer contains 12 red and 12 blue socks, all unmatched. A person takes socks out at random in the dark. How many socks must he take out to be sure that he has at least two blue socks?
Solution:
To find the minimum number of socks the person must take out to be sure of having at least two blue socks, we need to consider the worst-case scenario. In this scenario, the person would have already picked out all the red socks before picking out any blue socks.
Step 1: Calculate the maximum number of red socks the person can pick out before picking out any blue socks.
Since there are 12 red socks and 12 blue socks, the person can pick out a maximum of 12 red socks before picking out any blue socks.
Step 2: Determine the number of additional socks the person needs to pick out to have at least two blue socks.
To have at least two blue socks, the person needs to pick out one blue sock (the first blue sock) and then another blue sock.
Therefore, the person needs to pick out a total of 2 blue socks.
Step 3: Calculate the total number of socks the person needs to pick out.
The person needs to pick out a maximum of 12 red socks and 2 blue socks.
Therefore, the person needs to pick out a total of 14 socks to be sure that he has at least two blue socks.
Hence, the correct answer is option 'D' - 14.
A drawer contains 12 red and 12 blue socks, all unmatched. A person takes socks out at random in the dark. How many socks must he take out to be sure that he has at least two blue socks?
Solution:
To find the minimum number of socks the person must take out to be sure of having at least two blue socks, we need to consider the worst-case scenario. In this scenario, the person would have already picked out all the red socks before picking out any blue socks.
Step 1: Calculate the maximum number of red socks the person can pick out before picking out any blue socks.
Since there are 12 red socks and 12 blue socks, the person can pick out a maximum of 12 red socks before picking out any blue socks.
Step 2: Determine the number of additional socks the person needs to pick out to have at least two blue socks.
To have at least two blue socks, the person needs to pick out one blue sock (the first blue sock) and then another blue sock.
Therefore, the person needs to pick out a total of 2 blue socks.
Step 3: Calculate the total number of socks the person needs to pick out.
The person needs to pick out a maximum of 12 red socks and 2 blue socks.
Therefore, the person needs to pick out a total of 14 socks to be sure that he has at least two blue socks.
Hence, the correct answer is option 'D' - 14.
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Community Answer
A drawer contains 12 red and 12 blue socks, all unmatched. A person ta...
Given 12 red and 12 blue socks so, in order to take out at least 2 blue socks, first we need to take out 12 shocks (which might end up red in worst case) and then take out 2 socks (which would be definitely blue). Thus we need to take out total 14 socks.
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A drawer contains 12 red and 12 blue socks, all unmatched. A person takes socks out at random in the dark. How many socks must he take out to be sure that he has at least two blue socks?a)18b)35c)28d)14Correct answer is option 'D'. Can you explain this answer?
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