Three students are picked at random from a school having a total of 1000 students. The probability that these three students will have identical data and month of their birth is:

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Q: 147 (IAS/2004)
Three students are picked at random from a school having a total of 1000 students. The probability that these three students will have identical data and month of their birth is:

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,2,6,3,1,2,2

keywords: 

{'probability': [0, 3, 3, 0], 'students': [0, 1, 1, 1], 'identical data': [0, 0, 1, 0], 'birth': [11, 1, 4, 9], 'school': [3, 0, 1, 5], 'month': [9, 0, 7, 1]}

The correct answer is option 3, implying that the probability of the three students having the same date and month of birth is 1/(365)^2. Here`s why:

The first student can have a birthday on any day of the year, so cannot influence the probability. The next student though, if they are to have the same birthday, must have theirs on that exact day, creating a 1/365 chance. This probability holds for the third student as well.

The three probabilities must be multiplied together to find the overall probability (since they are independent events), which gives (1 x 1/365 x 1/365) = 1/(365^2).

Option 1 is incorrect because it assumes the students are chosen from the 1000 student population, not relevant to the date and month of birth.

Option 2 is incorrect as it considers the probabilities of only two students having the same birthdays.

Option 4 could be discarded as the correct answer is already given.

Therefore, option 3 is correct.

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