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It is dark in my bedroom and I want to get two socks of the same color from my drawer, which contains 24 red and 24 blue socks. How many socks do I have to take from the drawer to get at least two socks of the same color?
- a)2
- b)3
- c)48
- d)25
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
It is dark in my bedroom and I want to get two socks of the same color...
The Answer is 25. First he will select 24 in that the maximum chance is all are redm so if we take one more socks, it has to be the other color. Hence, the answer is 24 + 1 = 25
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It is dark in my bedroom and I want to get two socks of the same color...
Problem:
You are in a dark room and you want to get two socks of the same color from a drawer that contains 24 red and 24 blue socks. How many socks do you have to take from the drawer to guarantee that you have at least two socks of the same color?
Solution:
To solve this problem, we need to determine the minimum number of socks we need to take from the drawer to guarantee that we have at least two socks of the same color.
Step 1: Consider the Worst Case Scenario
To find the worst-case scenario, we assume that every sock we choose is of a different color from the ones we have already chosen. This means that for every new sock we pick, it must be of a different color from the previously chosen socks.
Step 2: Select the First Sock
Since we do not have any socks yet, the first sock we choose can be of any color. Therefore, we choose the first sock.
Step 3: Select the Second Sock
To guarantee that the second sock is of a different color from the first one, we need to choose a sock of the opposite color. In this case, since we have chosen the first sock, we need to choose a sock of the opposite color, which is the second color available in the drawer.
Step 4: Determine the Minimum Number of Socks
To guarantee that we have at least two socks of the same color, we need to consider the worst-case scenario. In this scenario, we have chosen one sock of each color. Therefore, we need to continue choosing socks until we have chosen at least one sock of the same color as the ones we have already chosen.
Step 5: Calculate the Minimum Number of Socks
In the worst-case scenario, we have chosen one sock of each color. Since there are 24 red and 24 blue socks in the drawer, the minimum number of socks we need to choose to guarantee at least two socks of the same color is 24 + 1 + 1 = 26.
Step 6: Verify the Correct Answer
According to the options given, option 'D' states that you need to take 25 socks from the drawer to get at least two socks of the same color. However, this is not correct because in the worst-case scenario, you need to take at least 26 socks to guarantee this condition.
Therefore, the correct answer is option 'D'.
You are in a dark room and you want to get two socks of the same color from a drawer that contains 24 red and 24 blue socks. How many socks do you have to take from the drawer to guarantee that you have at least two socks of the same color?
Solution:
To solve this problem, we need to determine the minimum number of socks we need to take from the drawer to guarantee that we have at least two socks of the same color.
Step 1: Consider the Worst Case Scenario
To find the worst-case scenario, we assume that every sock we choose is of a different color from the ones we have already chosen. This means that for every new sock we pick, it must be of a different color from the previously chosen socks.
Step 2: Select the First Sock
Since we do not have any socks yet, the first sock we choose can be of any color. Therefore, we choose the first sock.
Step 3: Select the Second Sock
To guarantee that the second sock is of a different color from the first one, we need to choose a sock of the opposite color. In this case, since we have chosen the first sock, we need to choose a sock of the opposite color, which is the second color available in the drawer.
Step 4: Determine the Minimum Number of Socks
To guarantee that we have at least two socks of the same color, we need to consider the worst-case scenario. In this scenario, we have chosen one sock of each color. Therefore, we need to continue choosing socks until we have chosen at least one sock of the same color as the ones we have already chosen.
Step 5: Calculate the Minimum Number of Socks
In the worst-case scenario, we have chosen one sock of each color. Since there are 24 red and 24 blue socks in the drawer, the minimum number of socks we need to choose to guarantee at least two socks of the same color is 24 + 1 + 1 = 26.
Step 6: Verify the Correct Answer
According to the options given, option 'D' states that you need to take 25 socks from the drawer to get at least two socks of the same color. However, this is not correct because in the worst-case scenario, you need to take at least 26 socks to guarantee this condition.
Therefore, the correct answer is option 'D'.
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